Elastic properties of mono- and poly-crystalline PbO-type FeSe1−xTex (x = 0–1.0): A first-principles study

The structural parameters of the alloys are obtained as non-magnetic cases for which justification is provided. The elastic coefficients and various moduli of the monocrystalline FeSe_1−xTe_x system as a function of doping are predicted for the first time using density functional method. The bulk moduli, shear moduli, Young’s moduli, Poisson’s ratios, velocities of sound and Debye temperature of the corresponding poly-crystalline aggregates have been calculated and the results discussed.     

Intersection numbers on Grassmannians,and on the space of holomorphic maps from CP1 into Gr(Cn)

We derive some explicit expressions for correlators on Grassmannian G_r(Cⁿ) as well as on the moduli space of holomorphic maps, of a fixed degree d, from sphere into the Grassmannian. Correlators obtained on the Grassmannian are a first-step generalization of the Schubert formula for the self-intersection. The intersection numbers on the moduli space for r=2,3 are given explicitly by two closed formulas, when r=2 the intersection numbers are found to generate the alternate Fibonacci numbers, the Pell numbers and in general a random walk of a particle on a line with absorbing barriers. For r=3, the intersection numbers form a well-organized pattern.     

On the adelic string amplitudes

Some remarkable properties of the adelic string amplitudes for the physical domain of the Mandelstam variables are considered. It is shown that the p-adic four-point functions are always negative. Also, a formula is obtained which expresses the product of moduli of the p-adic amplitudes and the Veneziano amplitude in terms of the zeta functions. This product is absolutely convergent unlike the divergent product of these amplitudes without moduli, recently considered by Freund and Witten. Using the zeta function representation, p-adic interpolation of the Veneziano amplitude is also considered.     

Observations on the moduli space of superconformal field theories

Some aspects of the moduli space of superconformal field theories are discussed. It is helpful to consider the conformal field theory as a background for propagation of strings and to exploit the space-time interpretation. Using this point of view we show that the metric on the moduli space of N = 4 superconformal field theory with c = 6 is locally that of O(20,4)/O(20) × O(4). We also discover some properties of the moduli space of N = 2 superconformal field theories with c = 9. Particular examples of these conformal field theories are sigma models on four- and six-dimensional Calabi-Yau spaces. Therefore, we can use this technique to learn about the moduli space of these spaces. For c = 6 we recover the known moduli space of K₃. Our analysis of the c = 9 system leads to a new coupling in four dimensional supergravity. As a by-product, we prove that gauge couplings cannot depend on the moduli of N = 1 space-time supersymmetric compactifications.     

The elastic moduli and their pressure and temperature derivatives for calcium oxide

The room temperature adiabatic elastic moduli of CaO were obtained using a pulse superposition technique to measure the ultrasonic velocities. The elastic moduli were found to be (in GPa) at 298 K.

     

6.

D-branes on group manifolds     

《Nuclear Physics B》1997,499(3):583-595

Possible Dirichlet boundary states for WZW models with untwisted affine super Kac-Moody symmetry are classified for all compact simple Lie groups. They are obtained by inner- and outerautomorphisms of the group. The D-brane world-volume turns out to be a group manifold of a symmetric subgroup, so that the moduli space of D-branes is locally isomorphic to an irreducible Riemannian symmetric space. It is also clarified how these D-branes are transformed into each other under abelian T-duality of the WZW model. Our result implies, for example, that there is no D-particle on the compact simple group manifold. When the D-brane world-volume contains an S¹ factor, the D-brane moduli space becomes locally isomorphic to a hermitian symmetric space and open string world-sheet instantons are allowed.     

7.

Theoretical study of the dependences of the young’s and torsion moduli of thin single-layer carbon zigzag and armchair nanotubes on the geometric parameters     

O. E. Glukhova  O. A. Terent’ev 《Physics of the Solid State》2006,48(7):1411-1417

The Young’s and torsion moduli of single-layer carbon (m, 0) and (m, m) nanotubes are studied. It is demonstrated that both moduli depend on the chirality, diameter, and length of the nanotube. It is found for the first time that the torsion modulus increases with the nanotube diameter and diminishes with an increase in its length. By considering nanotubes with various values of the diameter-to-length ratio, it is shown that the Young’s and torsion moduli of the nanotubes saturate at a diameter-to-length ratio of ～0.3. The values of the torsion modulus as calculated from the Young’s modulus we obtained and from the deformation energy do not coincide, which can be attributed to the effect of dangling bonds at the open ends of the nanotubes. Energy calculations are performed using the Goodwin modification of the semiempirical Harrison tight-binding method.     

8.

Instanton strings and hyper-Kähler geometry     

《Nuclear Physics B》1999,543(3):545-571

We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N = (4, 4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS³. We derive a precise map relating the moduli of the K3 type 1113 string compactification to the moduli of these conformal field theories and the corresponding classical hyper-Kahler geometry. We conclude that in the absence of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyper-Kähler manifolds.     

9.

Structural,elastic, electronic properties and Fermi surface for superconducting Mo2GaC in comparison with V2GaC and Nb2GaC from first principles     

I.R. Shein  A.L. Ivanovskii 《Physica C: Superconductivity and its Applications》2010,470(13-14):533-537

First-principles calculations were performed to investigate structural, elastic and electronic properties of the first discovered superconducting nanolaminate Mo₂GaC in comparison with isostructural Ga-containing phases V₂GaC and Nb₂GaC. As a result, the optimized lattice parameters, independent elastic constants, bulk moduli, compressibility, shear moduli, Young’s moduli and Poisson’s ratio were evaluated. Besides, electronic bands, densities of states (DOS), total and site-projected l-decomposed DOS at the Fermi level, as well as the shapes of the Fermi surfaces for these Ga-containing nanolaminates were obtained and analyzed in comparison with the available theoretical and experimental data.     

10.

Dependence of lattice constants and bulk moduli on pseudopotential properties     

Pui K. Lam  Marvin L. Cohen 《Physics letters. A》1984,100(6):293-296

Using a nearly-free-electron model and model pseudopotentials, an analytical relation between the Wigner-Seitz radius for a metal, r_ws, and the core radius of the model pseudopotential, r_c is derived. In addition, a semi-empirical formula for the bulk moduli is obtained.     

11.

Two-loop statsum of superstrings     

《Nuclear Physics B》1988,303(2):343-372

We discuss, whether there is a choice of odd moduli on super-Riemann surfaces of genus p≳2, which leads to the vanishing of statistical sums of superstrings before integration over the space of even moduli. The answer is shown to be positive at least for p=2, when odd moduli are localized at ramification points. The relation between various definitions of many-loop statistical sums in superstring theory is discussed.     

12.

A string calculation of the Kähler potentials for moduli of ZN orbifolds     

《Physics letters. [Part B]》1988,206(2):227-233

We present a method for calculating the Kähler potentials of the moduli of Z_N orbifolds directly from string theory. The explicit Kähler potentials associated with b_(1,1) and b_(1,2) moduli are given for any (2,0) symmetric Z_N orbifold. These results are exact at the string tree level.     

13.

Bethe ansatz study of two-dimensional soliton lattice melting     

S. Park  K. Moon 《Solid State Communications》2004,132(12):851-856

We study the melting of incommensurate soliton lattice using the exact Bethe ansatz solution of one-dimensional quantum sine-Gordon Hamiltonian with U(1) coupling. The elastic moduli of soliton lattice are obtained and their asymptotic behaviors are explicitly calculated both at zero and finite temperature. We have obtained the thermodynamic phase boundaries of the soliton lattice and shown that the direct commensurate-incommensurate transitions are intervened by the fluid phase for T>0 as predicted by Coppersmith et al. [Coppersmith et al., Phys. Rev. Lett. 46 (1981) 549. [1]] for n≤2.     

14.

Vibrational spectra and elastic,piezoelectric, and magnetoelectric properties of HoFe3(BO3)4 and HoAl3(BO3)4 crystals     

V. I. Zinenko  M. S. Pavlovskii  A. S. Krylov  I. A. Gudim  E. V. Eremin 《Journal of Experimental and Theoretical Physics》2013,117(6):1032-1041

Raman spectra of light are obtained for HoFe₃(BO₃)₄ and HoAl₃(BO₃)₄ crystals at various temperatures and are used for determining the frequencies of crystal lattice vibrations at the center of the Brillouin zone. It is also found that the HoFe₃(BO₃)₄ crystal exhibits a phase transition at T _c ≈ 366 K. The magnetoelectric effect in the paramagnetic phase of these compounds is studied experimentally. The lattice vibration frequencies, elastic and piezoelectric moduli, Born dynamic charges, and the high-frequency permittivity are calculated using the density functional method. A peculiar behavior of the transverse acoustic vibration branch is observed in the Γ → Z direction of the Brillouin zone of the HoFe₃(BO₃)₄ crystal. The electric polarization induced by an external field is estimated using the calculated values of piezoelectric moduli and experimental values of magnetostriction.     

15.

Ultrasonic studies on alkali borate tungstate glasses     

M.S. Gaafar  Y.B. Saddeek 《Journal of Physics and Chemistry of Solids》2009,70(1):173-800

Longitudinal and shear ultrasonic wave velocities have been measured in different compositions of the glass system 20Li₂O-(80−x)B₂O₃-xWO₃ (0?x?12.5 mol%), at room temperature and at 4 MHz frequency. Elastic moduli, Debye temperature and Poisson's ratio have been obtained as a function of WO₃ content. Based on FTIR spectroscopy and theoretical bond compression model, quantitative analysis has been carried out in order to obtain more information about the structure of these glasses. The longitudinal ultrasonic wave velocity measurements showed a bend at about 2.5 mol% WO₃ content while shear ultrasonic wave velocity decreased monotonously with an increase of WO₃ content. Elastic moduli values decreased as WO₃ content increased from 0 to 2.5 mol%. Further increase of WO₃ beyond 2.5 mol% increased the elastic moduli values. It is suggested that these behaviours are mainly due to the presence of WO₃ in the network structure of these glasses as a network modifier when WO₃ content is between 0 and 2.5 mol%, and acts as a network former above 2.5 mol%.     

16.

The prequantum line bundle on the moduli space of flat <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) connections on a Riemann surface and the homotopy of the large <Emphasis Type="Italic">N</Emphasis> limit     

Lisa C. Jeffrey  Daniel A. Ramras  Jonathan Weitsman 《Letters in Mathematical Physics》2017,107(9):1581-1589

We show that the prequantum line bundle on the moduli space of flat SU(2) connections on a closed Riemann surface of positive genus has degree 1. It then follows from work of Lawton and the second author that the classifying map for this line bundle induces a homotopy equivalence between the stable moduli space of flat SU(n) connections, in the limit as n tends to infinity, and \( {\mathbb C}P^\infty \). Applications to the stable moduli space of flat unitary connections are also discussed.     

17.

Hydrostatic pressure derivatives of the single crystal elastic moduli of Gd,Dy and Er     

E.S. Fisher  M.H. Manghnani  R. Kikuta 《Journal of Physics and Chemistry of Solids》1973,34(4):687-703

The hydrostatic pressure derivatives of the single crystal elastic moduli of Gd, Dy and Er have been measured at 298°K, to pressures near 5 Kbar. The very small pressure derivatives of the adiabatic bulk moduli indicate that a small ion core model should be appropriate for interpreting the data. The long-range electrostatic contributions to the shear moduli have a dominant influence on the pressure derivatives of the shear moduli of Er, whereas the Gd and Dy data evidently reflect band structure contributions. The values of the longitudinal stiffnesses correspond remarkably well with the Bohm-Staver model for velocity of waves in an ion plasma dispersed in a sea of electrons, where the ionic interaction is perely Coulombic. This model is extended to provide an interpretation of the volume derivatives of the longitudinal moduli in terms of the volume derivative of the density of electron states at the Fermi energy.The Grüneisen parameters calculated from averages of the acoustic model gammas are in relatively poor agreement with those determined from thermal expansion data. An explanation based on the changes in c/a ratio with volume change is tested quantitatively and found to be reasonably successful. The values of dK_T/dP, where K_T is the isothermal bulk modulus, are applied to the Murnaghan equation of state and give excelent agreement with Bridgman's direct compression data for Dy and Er to 40 Kbar. For Gd, Bridgman's data indicate either that (dK_T/dP)_p=0 should be considerably larger than deduced from the adiabatic dK_s/dP measurements or that a phase change occurs near 20 Kbar. The occurrence of a phase change in Er at ～90 Kbar is definitely indicated when comparing the Murnaghan equation with X-ray diffraction data.     

18.

Spectral Networks and Fenchel–Nielsen Coordinates     

Lotte Hollands  Andrew Neitzke 《Letters in Mathematical Physics》2016,106(6):811-877

It is known that spectral networks naturally induce certain coordinate systems on moduli spaces of flat SL(K)-connections on surfaces, previously studied by Fock and Goncharov. We give a self-contained account of this story in the case K = 2 and explain how it can be extended to incorporate the complexified Fenchel–Nielsen coordinates. As we review, the key ingredient in the story is a procedure for passing between moduli of flat SL(2)-connections on C (equipped with a little extra structure) and moduli of equivariant GL(1)-connections over a covering \({\Sigma \to C}\); taking holonomies of the equivariant GL(1)-connections then gives the desired coordinate systems on moduli of SL(2)-connections. There are two special types of spectral network, related to ideal triangulations and pants decompositions of C; these two types of network lead to Fock–Goncharov and complexified Fenchel–Nielsen coordinate systems, respectively.     

19.

Bundle gerbes and moduli spaces     

Peter Bouwknegt  Varghese Mathai  Siye Wu 《Journal of Geometry and Physics》2012,62(1):1-10

In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analytically constructed index bundle gerbe. We apply these constructions to certain moduli spaces associated to compact Riemann surfaces, constructing on these moduli spaces, natural bundle gerbes with connection and curving, whose 3-curvature represent Dixmier-Douady classes that are generators of the third de Rham cohomology groups of these moduli spaces.     

20.

Moduli matrices of the vacua and walls on SO(2N)/U(N)     

M. Arai  Su. Shin 《Physics of Particles and Nuclei》2012,43(5):652-653

We construct parallel domain walls on the SO(2N)/U(N) manifold by using the moduli matrices, which were originally formulated on the Grassmann manifold. We propose a method to impose a quadratic constraint to the moduli matrices. This talk is based on [3]PRD83,125003(2011). This article is prepared for the proceedings of International Workshop on Supersymmetries and Quantum Symmetries-SQS 2011.     

c11	c12	c44
226.2 ±0.9	62.4 ±0.9	80.6 ±0.3 The pressure derivatives of the elastic moduli, which were measured at and below room temperature, decrease with decreasing temperature. The temperature derivatives of the elastic moduli were also obtained for several temperatures below room temperature.

D-branes on group manifolds

Possible Dirichlet boundary states for WZW models with untwisted affine super Kac-Moody symmetry are classified for all compact simple Lie groups. They are obtained by inner- and outerautomorphisms of the group. The D-brane world-volume turns out to be a group manifold of a symmetric subgroup, so that the moduli space of D-branes is locally isomorphic to an irreducible Riemannian symmetric space. It is also clarified how these D-branes are transformed into each other under abelian T-duality of the WZW model. Our result implies, for example, that there is no D-particle on the compact simple group manifold. When the D-brane world-volume contains an S¹ factor, the D-brane moduli space becomes locally isomorphic to a hermitian symmetric space and open string world-sheet instantons are allowed.     

Theoretical study of the dependences of the young’s and torsion moduli of thin single-layer carbon zigzag and armchair nanotubes on the geometric parameters

The Young’s and torsion moduli of single-layer carbon (m, 0) and (m, m) nanotubes are studied. It is demonstrated that both moduli depend on the chirality, diameter, and length of the nanotube. It is found for the first time that the torsion modulus increases with the nanotube diameter and diminishes with an increase in its length. By considering nanotubes with various values of the diameter-to-length ratio, it is shown that the Young’s and torsion moduli of the nanotubes saturate at a diameter-to-length ratio of ～0.3. The values of the torsion modulus as calculated from the Young’s modulus we obtained and from the deformation energy do not coincide, which can be attributed to the effect of dangling bonds at the open ends of the nanotubes. Energy calculations are performed using the Goodwin modification of the semiempirical Harrison tight-binding method.     

Instanton strings and hyper-Kähler geometry

We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N = (4, 4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS³. We derive a precise map relating the moduli of the K3 type 1113 string compactification to the moduli of these conformal field theories and the corresponding classical hyper-Kahler geometry. We conclude that in the absence of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyper-Kähler manifolds.     

Structural,elastic, electronic properties and Fermi surface for superconducting Mo2GaC in comparison with V2GaC and Nb2GaC from first principles

First-principles calculations were performed to investigate structural, elastic and electronic properties of the first discovered superconducting nanolaminate Mo₂GaC in comparison with isostructural Ga-containing phases V₂GaC and Nb₂GaC. As a result, the optimized lattice parameters, independent elastic constants, bulk moduli, compressibility, shear moduli, Young’s moduli and Poisson’s ratio were evaluated. Besides, electronic bands, densities of states (DOS), total and site-projected l-decomposed DOS at the Fermi level, as well as the shapes of the Fermi surfaces for these Ga-containing nanolaminates were obtained and analyzed in comparison with the available theoretical and experimental data.     

Dependence of lattice constants and bulk moduli on pseudopotential properties

Using a nearly-free-electron model and model pseudopotentials, an analytical relation between the Wigner-Seitz radius for a metal, r_ws, and the core radius of the model pseudopotential, r_c is derived. In addition, a semi-empirical formula for the bulk moduli is obtained.     

Two-loop statsum of superstrings

We discuss, whether there is a choice of odd moduli on super-Riemann surfaces of genus p≳2, which leads to the vanishing of statistical sums of superstrings before integration over the space of even moduli. The answer is shown to be positive at least for p=2, when odd moduli are localized at ramification points. The relation between various definitions of many-loop statistical sums in superstring theory is discussed.     

A string calculation of the Kähler potentials for moduli of ZN orbifolds

We present a method for calculating the Kähler potentials of the moduli of Z_N orbifolds directly from string theory. The explicit Kähler potentials associated with b_(1,1) and b_(1,2) moduli are given for any (2,0) symmetric Z_N orbifold. These results are exact at the string tree level.     

Bethe ansatz study of two-dimensional soliton lattice melting

We study the melting of incommensurate soliton lattice using the exact Bethe ansatz solution of one-dimensional quantum sine-Gordon Hamiltonian with U(1) coupling. The elastic moduli of soliton lattice are obtained and their asymptotic behaviors are explicitly calculated both at zero and finite temperature. We have obtained the thermodynamic phase boundaries of the soliton lattice and shown that the direct commensurate-incommensurate transitions are intervened by the fluid phase for T>0 as predicted by Coppersmith et al. [Coppersmith et al., Phys. Rev. Lett. 46 (1981) 549. [1]] for n≤2.     

Vibrational spectra and elastic,piezoelectric, and magnetoelectric properties of HoFe3(BO3)4 and HoAl3(BO3)4 crystals

Raman spectra of light are obtained for HoFe₃(BO₃)₄ and HoAl₃(BO₃)₄ crystals at various temperatures and are used for determining the frequencies of crystal lattice vibrations at the center of the Brillouin zone. It is also found that the HoFe₃(BO₃)₄ crystal exhibits a phase transition at T _c ≈ 366 K. The magnetoelectric effect in the paramagnetic phase of these compounds is studied experimentally. The lattice vibration frequencies, elastic and piezoelectric moduli, Born dynamic charges, and the high-frequency permittivity are calculated using the density functional method. A peculiar behavior of the transverse acoustic vibration branch is observed in the Γ → Z direction of the Brillouin zone of the HoFe₃(BO₃)₄ crystal. The electric polarization induced by an external field is estimated using the calculated values of piezoelectric moduli and experimental values of magnetostriction.     

Ultrasonic studies on alkali borate tungstate glasses

Longitudinal and shear ultrasonic wave velocities have been measured in different compositions of the glass system 20Li₂O-(80−x)B₂O₃-xWO₃ (0?x?12.5 mol%), at room temperature and at 4 MHz frequency. Elastic moduli, Debye temperature and Poisson's ratio have been obtained as a function of WO₃ content. Based on FTIR spectroscopy and theoretical bond compression model, quantitative analysis has been carried out in order to obtain more information about the structure of these glasses. The longitudinal ultrasonic wave velocity measurements showed a bend at about 2.5 mol% WO₃ content while shear ultrasonic wave velocity decreased monotonously with an increase of WO₃ content. Elastic moduli values decreased as WO₃ content increased from 0 to 2.5 mol%. Further increase of WO₃ beyond 2.5 mol% increased the elastic moduli values. It is suggested that these behaviours are mainly due to the presence of WO₃ in the network structure of these glasses as a network modifier when WO₃ content is between 0 and 2.5 mol%, and acts as a network former above 2.5 mol%.     

The prequantum line bundle on the moduli space of flat <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) connections on a Riemann surface and the homotopy of the large <Emphasis Type="Italic">N</Emphasis> limit

We show that the prequantum line bundle on the moduli space of flat SU(2) connections on a closed Riemann surface of positive genus has degree 1. It then follows from work of Lawton and the second author that the classifying map for this line bundle induces a homotopy equivalence between the stable moduli space of flat SU(n) connections, in the limit as n tends to infinity, and \( {\mathbb C}P^\infty \). Applications to the stable moduli space of flat unitary connections are also discussed.     

Hydrostatic pressure derivatives of the single crystal elastic moduli of Gd,Dy and Er

The hydrostatic pressure derivatives of the single crystal elastic moduli of Gd, Dy and Er have been measured at 298°K, to pressures near 5 Kbar. The very small pressure derivatives of the adiabatic bulk moduli indicate that a small ion core model should be appropriate for interpreting the data. The long-range electrostatic contributions to the shear moduli have a dominant influence on the pressure derivatives of the shear moduli of Er, whereas the Gd and Dy data evidently reflect band structure contributions. The values of the longitudinal stiffnesses correspond remarkably well with the Bohm-Staver model for velocity of waves in an ion plasma dispersed in a sea of electrons, where the ionic interaction is perely Coulombic. This model is extended to provide an interpretation of the volume derivatives of the longitudinal moduli in terms of the volume derivative of the density of electron states at the Fermi energy.The Grüneisen parameters calculated from averages of the acoustic model gammas are in relatively poor agreement with those determined from thermal expansion data. An explanation based on the changes in c/a ratio with volume change is tested quantitatively and found to be reasonably successful. The values of dK_T/dP, where K_T is the isothermal bulk modulus, are applied to the Murnaghan equation of state and give excelent agreement with Bridgman's direct compression data for Dy and Er to 40 Kbar. For Gd, Bridgman's data indicate either that (dK_T/dP)_p=0 should be considerably larger than deduced from the adiabatic dK_s/dP measurements or that a phase change occurs near 20 Kbar. The occurrence of a phase change in Er at ～90 Kbar is definitely indicated when comparing the Murnaghan equation with X-ray diffraction data.     

Spectral Networks and Fenchel–Nielsen Coordinates

It is known that spectral networks naturally induce certain coordinate systems on moduli spaces of flat SL(K)-connections on surfaces, previously studied by Fock and Goncharov. We give a self-contained account of this story in the case K = 2 and explain how it can be extended to incorporate the complexified Fenchel–Nielsen coordinates. As we review, the key ingredient in the story is a procedure for passing between moduli of flat SL(2)-connections on C (equipped with a little extra structure) and moduli of equivariant GL(1)-connections over a covering \({\Sigma \to C}\); taking holonomies of the equivariant GL(1)-connections then gives the desired coordinate systems on moduli of SL(2)-connections. There are two special types of spectral network, related to ideal triangulations and pants decompositions of C; these two types of network lead to Fock–Goncharov and complexified Fenchel–Nielsen coordinate systems, respectively.     

Bundle gerbes and moduli spaces

In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analytically constructed index bundle gerbe. We apply these constructions to certain moduli spaces associated to compact Riemann surfaces, constructing on these moduli spaces, natural bundle gerbes with connection and curving, whose 3-curvature represent Dixmier-Douady classes that are generators of the third de Rham cohomology groups of these moduli spaces.     

Moduli matrices of the vacua and walls on SO(2N)/U(N)

We construct parallel domain walls on the SO(2N)/U(N) manifold by using the moduli matrices, which were originally formulated on the Grassmann manifold. We propose a method to impose a quadratic constraint to the moduli matrices. This talk is based on [3]PRD83,125003(2011). This article is prepared for the proceedings of International Workshop on Supersymmetries and Quantum Symmetries-SQS 2011.