Seiberg-Witten geometry with various matter contents

We obtain the Seiberg-Witten geometry for four-dimensional N = 2 gauge theory with gauge group SO(2N_c) (N_c ⩽ 5) with massive spinor and vector hypermultiplets by considering the gauge symmetry breaking in the N = 2 E₆ theory with massive fundamental hypermultiplets. In a similar way the Seiberg-Witten geometry is determined for N = 2 SU(N_c) (N_c ⩽ 6) gauge theory with massive antisymmetric and fundamental hypermultiplets. Whenever possible we compare our results expressed in the form of ALE fibrations with those obtained by geometric engineering and brane dynamics, and find a remarkable agreement. We also show that these results are reproduced by using N = 1 confining phase superpotentials.     

Some aspects of a unified approach to gauge,dual and Gribov theories

We consider quantum chromodynamics (QCD) with N_c colours and N_f flavours. Large N expansions for this theory are discussed and their advantages are pointed out, especially in relation to the possibility of unifying gauge, dual and Gribov theories of strong interactions. We first recall how the 1/N_c expansion of 't Hooft can be related to a dual loop expansion with a fixed coupling constant. We point out the necessity for quarkless (purely gluonic) bound states to appear and their importance in maintaining confinement at higher orders in 1/N_c. We show how non-orientable dual loops are reinterpreted in QCD and how a paradox appears when N_f is such that asymptotic freedom is lost. Some recent results of Cornwall and Tiktopoulos are analyzed in leading order in 1/N_c. We then introduce a 1/N expansion at ? ≡ N_f/N_c fixed and show how it is related to the hadronic topological expansion (TE). This allows an unambiguous definition of reggeon field theory concepts such as the bare pomeron and diffractive dissociation in QDC. We are able to relate the parameter ? to the clustering of hadronic final states into resonances. Decreasing ? corresponds to increasing cluster over gap size. Renormalization of the dual coupling constant as a function of ? is discussed and an apparent paradox is resolved. We are also able to shed some new light on the problem of f extinction in the TE.Finally, we compare our approach to other schemes trying to relate different aspects of hadron physics.     

Electronic transport in graphene nanoribbons with disorder look at the pseudo-spin polarization: Dirac versus tight-binding model

We have compared results of electronic transport using two different approaches: Dirac vs tight-binding (TB) Hamiltonians to assesses disorder-induced effects in graphene nanoribbons. We apply the proposed Hamiltonians to calculate the density of states, the transmission along the ribbon, and the pseudo-spin polarization (P(E)) in metallic armchair graphene nanoribbons. We clearly show differences between these two approaches in the interference processes, especially in the low-lying energy limit, when the systems are found in the presence of random impurities (disorder). This allows us to find fingerprints associated with each model used. As the disorder increases, more robust electronic transmission (through polarized states in a given sublattice) arises when one is dealing with the Dirac model only. We also find with this model unexpected peaks in the P(E) far from the Dirac point for wider nanoribbons. In the other hand, the model TB show the Dirac limit with disturbances of the hyperboloid subbands for certain potentials of the impurities. In general, our study is indicating that a P(E) spectroscopy (analyzing the line width and intensity) can be used to detect fingerprints of the increase of asymmetry in the scattering processes and the transport limits where hyperboloid subbands are important.     

Relating c < 0 and c > 0 conformal field theories

A ‘canonical mapping’ is established between the c = −1 system of bosonic ghosts and the c = 2 complex scalar theory and a similar mapping between the c = −2 system of fermionic ghosts and the c = 1 Dirac theory. The existence of this mapping is suggested by the identity of the characters of the respective theories. The respective c < 0 and c > 0 theories share the same space of states, whereas the spaces of conformal fields are different. Upon this mapping from their c < 0 counterparts, the (c > 0) complex scalar and the Dirac theories inherit hidden non-local sl(2) symmetries.     

The Haldane-Rezayi quantum Hall state and conformal field theory

We propose field theories for the bulk and edge of a quantum Hall state in the universality class of the Haldane-Rezayi wavefunction. The bulk theory is associated with the c = −2 conformal field theory. The topological properties of the state, such as the quasiparticle braiding statistics and ground state degeneracy on a torus, may be deduced from this conformal field theory. The 10-fold degeneracy on a torus is explained by the existence of a logarithmic operator in the c = −2 theory; this operator corresponds to a novel bulk excitation in the quantum Hall state. We argue that the edge theory is the c = 1 chiral Dirac fermion, which is related in a simple way to the c = −2 theory of the bulk. This theory is reformulated as a truncated version of a doublet of Dirac fermions in which the SU(2) symmetry - which corresponds to the spin-rotational symmetry of the quantum Hall system - is manifest and non-local. We make predictions for the current-voltage characteristics for transport through point contacts.     

Holomorphy of the scattering matrix with respect toc −2 for Dirac operators and an explicit treatment of relativistic corrections

We prove holomorphy of the scattering matrix at fixed energy with respect toc ^–2 for abstract Dirac operators. Relativistic corrections of orderc ^–2 to the nonrelativistic limit scattering matrix (associated with an abstract Pauli Hamiltonian) are explicitly determined. As applications of our abstract approach we discuss concrete realizations of the Dirac operator in one and three dimensions and explicitly compute relativistic corrections of orderc ^–2 of the reflection and transmission coefficients in one dimension and of the scattering matrix in three dimensions. Moreover, we give a comparison between our approach and the firstorder relativistic corrections according to Foldy-Wouthuysen scattering theory and show complete agreement of the two methods.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich by an E. Schrödinger Fellowship and by Project No. P7425     

A criterion for percolation threshold in a random array of plates

We give a dimensionless criterion for percolation of a random assembly of 3-dimensional flat disks of radius r with a density N per unit volume as (Nr³)_c ～0.15 to 0.3. The invariant at threshold is obtained by analogy with excluded volume results for arrays of needles or with the active filling factor approach used for spheres. As the result can be applied to the permeability of fractured rocks, we discuss the results for polydisperse assemblies and we show how the invariant can be measured from a random cut of the array of disks.     

Relativistic versus nonrelativistic solution of the N-fermion problem in a hyperradius-confining potential

We investigate the quantum system of N identical fermions in the relativistic limit. In this article the considered potential is a combination of Coulombic, linear confining and harmonic oscillator terms. By using Jacobi coordinates and introducing the hyperradius quantity we obtain the wave functions of the system as well as the corresponding energy eigenvalues. Assuming that all particles are confined within a hypersphere we calculate the corresponding x _bag . In particular we consider the case N = 3 which corresponds to baryonic systems. By using the experimental values of the charge radius of each baryon we calculate the potential coefficients. Within our treatment the results of the MIT bag model are recovered for N = 1. Finally we compare the results obtained by the Dirac equation with the corresponding results of the Schrödinger equation and we find that the energy spectra obtained by the former are much closer to experimental values.     

Analysis of localization-delocalization transitions in corner-sharing tetrahedral lattices

We study the critical behavior of the Anderson localization-delocalization transition in corner-sharing tetrahedral lattices. We compare our results obtained by three different numerical methods namely the multifractal analysis, the Green resolvent method, and the energy-level statistics which yield the singularity strength, the decay length of the wave functions, and the (integrated) energy-level distribution, respectively. From these measures a finite-size scaling approach allows us to determine the critical parameters simultaneously. With particular emphasis we calculate the propagation of the statistical errors by a Monte-Carlo method. We find a high agreement between the results of all methods and we can estimate the highest critical disorder W _c = 14.474 (8) at energy E _c = ? 4.0 and the critical exponent ν = 1.565 (11). Our results agree with a previous study by Fazileh et al. [F. Fazileh, X. Chen, R.J. Gooding, K. Tabunshchyk, Phys. Rev. B 73, 035124 (2006)] but improve accuracy significantly.     

Reunion Probability of N Vicious Walkers: Typical and Large Fluctuations for Large N

We consider three different models of N non-intersecting Brownian motions on a line segment [0,L] with absorbing (model A), periodic (model B) and reflecting (model C) boundary conditions. In these three cases we study a properly normalized reunion probability, which, in model A, can also be interpreted as the maximal height of N non-intersecting Brownian excursions (called “watermelons” with a wall) on the unit time interval. We provide a detailed derivation of the exact formula for these reunion probabilities for finite N using a Fermionic path integral technique. We then analyze the asymptotic behavior of this reunion probability for large N using two complementary techniques: (i) a saddle point analysis of the underlying Coulomb gas and (ii) orthogonal polynomial method. These two methods are complementary in the sense that they work in two different regimes, respectively for $L\ll O(\sqrt{N})$ and $L\geq O(\sqrt{N})$ . A striking feature of the large N limit of the reunion probability in the three models is that it exhibits a third-order phase transition when the system size L crosses a critical value $L=L_{c}(N)\sim\sqrt{N}$ . This transition is akin to the Douglas-Kazakov transition in two-dimensional continuum Yang-Mills theory. While the central part of the reunion probability, for L～L _c (N), is described in terms of the Tracy-Widom distributions (associated to GOE and GUE depending on the model), the emphasis of the present study is on the large deviations of these reunion probabilities, both in the right [L?L _c (N)] and the left [L?L _c (N)] tails. In particular, for model B, we find that the matching between the different regimes corresponding to typical L～L _c (N) and atypical fluctuations in the right tail L?L _c (N) is rather unconventional, compared to the usual behavior found for the distribution of the largest eigenvalue of GUE random matrices. This paper is an extended version of (Schehr et al. in Phys. Rev. Lett. 101:150601, 2008) and (Forrester et al. in Nucl. Phys. B 844:500–526, 2011).     

Dirac constraint analysis and symplectic structure of anti-self-dual Yang-Mills equations

We present the explicit form of the symplectic structure of anti-self-dual Yang-Mills (ASDYM) equations in Yang’s J- and K-gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac’s theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints are second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang-Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both J- and K-gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten-Zuckerman formalism. We show that the appropriate component of the Witten-Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac’s theory. Finally, we present the Bäcklund transformation between the J- and K-gauges in order to apply Magri’s theorem to the respective two Hamiltonian structures.     

Comments on mesonic correlators in the worldline formalism

We elaborate on how to incorporate mesonic correlators into the worldline formalism. We consider possible applications to QCD-like theories in various dimensions. We focus on large-Nc two-dimensional QCD (the ?t Hooft model) and relate it to a single harmonic oscillator. We also discuss the dependence of the Peskin S-parameter on the number of massless flavors and their representation and compare our expression to the corresponding expression obtained at weak coupling. Finally, we use the worldline formalism to discuss how the Veneziano limit of QCD is realized in holography in the limit of small Nf/Nc.     

Remark on the application of the effective hamiltonian method for random systems

We compare two versions of the effective Hamiltonian method applied to random bond systems. In one randomness is treated in a kind of the mean field approximation, whereas in the other the relevant arrangements of bonds are explicitly accounted for. Calculations for three dimensional systems of mixed ferromagnetic Heisenberg and Ising bonds show that although the T_c vs p (concentration of Heisenberg-loke interactions) curve in the second approach lies closer to the results of high temperature series general features in both approxsimations are quite similar.     

Spontaneous compactification and CPN: SU(3) × SU(2) × U(1), sin2θW, g3/g2 and SU(3)-triplet chiral fermions in four dimensions

We examine the compactification of D=4+2N, Einstein-Maxwell-Dirac theory. It is shown that the manifold CP_N × M₄ is a solution of the equations of motion. The structure of the fermions, gauge bosons and their couplings in the four-dimensional effective theory is investigated. The scale of CP_N is quantized by a generalized Dirac condition. When the results are applied to the solution with internal space CP₁×CP₂, the weak mixing angle and the ratio of the couplings of SU(3) (g₃) and SU(2) (g₂) are defined by two integers and a hypercharge. An SU(3)-triplet chiral fermion can appear in four-dimensional effective theory.     

Electron density of states and superconducting Tc in A15-compounds

We compare the superconductivity parameters of V₃Ga and V₃Ge by the method of McMillan with the help of new neutron diffraction data obtained by P. Schweiss. We consider the strongly varying density of states in V₃Ga at the Fermi energy, a complication suggested by Labbé, Barisic, and Friedel. We find that increased electronic density of states contributes about equally with lattice softening to the enhancement of T_c in V₃Ga as compared to V₃Ge, although the values of N(O)J² = Mλ〈ω²〉 are roughly consistent with those obtained for some other metals by McMillan. The reason N(O) is not more effective in raising T_c is the partial compensation obtained from averaging over the narrow density-of-states peak which gives N ? 0.6N(O).     

Logarithmic correlation functions in two-dimensional turbulence

We consider the correlation functions of two-dimensional turbulence in the presence and absence of a three-dimensional perturbation, by means of conformal field theory. In the presence of three-dimensional perturbation, we show that in the strong coupling limit of a small scale random force, there is some logarithmic factor in the correlation functions of velocity stream functions. We show that the logarithmic conformal field theory c_8,1 describes the 2D-turbulence both in the absence and in the presence of the perturbation. We obtain the energy spectrum E(k) ∼ k^−5.125 ln(k) for perturbed 2D-turbulence and E(k) ∼ k⁻⁵ ln(k) for unperturbed turbulence. Recent numerical simulation and experimental results confirm our prediction.     

Baryons in chiral SU(N)—QCD on the light-cone in 1 + 1-dimensions

We demonstrate that using bosonization techniques in 1+1-dimensional QCD in the chiral limit a unique definition of baryons is possible for finiteN _c despite the fact that mesons, baryons and anti-baryons are massless. The definition which is based on the construction of an SU(2)-algebra provides the basis for a new approach to investigate hadronic properties in the strong coupling limit. It is used to study the Fock-state decomposition and structure functions of baryons for various finite values ofN _c . The results are discussed in comparison to similar calculations based on discretized lightcone quantization.     

Non-hermitian random matrix models

We introduce an extension of the diagrammatic rules in random matrix theory and apply it to non-hermitian random matrix models using the 1/N approximation. A number of one-and two-point functions are evaluated on their holomorphic and non-holomorphic supports to leading order in 1/N. The one-point functions describe the distribution of eigenvalues, while the two-point functions characterize their macroscopic cotrelations. The generic form for the two-point functions is obtained, generalizing the concept of macroscopic universality to non-hermitian random matrices. We show that the holomorphic and non-holomorphic one- and two-point functions condition the behavior of pertinent partition functions to order O(1/N). We derive explicit conditions for the location and distribution of their singularities. Most of our analytical results are found to be in good agreement with numerical calculations using large ensembles of complex matrices.     

Disordered Dirac fermions: Multifractality termination and logarithmic conformal field theories

We reexamine in detail the problem of fermions interacting with a non-Abelian random vector potential. Without resorting to the replica or supersymmetry approaches, we show that in the limit of infinite disorder strength the theory possesses an exact solution which takes the form of a logarithmic conformal field theory. We show that the proper treatment of the locality conditions in the SU(2) theory leads to the termination of the multifractal spectrum, or in other words to the termination of the infinite hierarchies of negative-dimensional operators that were thought to occur. Based on arguments of logarithmic degeneracies, we conjecture that such a termination mechanism should be present for general SU(N). Moreover, our results lead to the conclusion that the previous replica solution of this problem yields incorrect results.