A modification of Einstein–Schrödinger theory that contains Einstein–Maxwell–Yang–Mills theory

The Lambda-renormalized Einstein–Schrödinger theory is a modification of the original Einstein–Schrödinger theory in which a cosmological constant term is added to the Lagrangian, and it has been shown to closely approximate Einstein– Maxwell theory. Here we generalize this theory to non-Abelian fields by letting the fields be composed of d × d Hermitian matrices. The resulting theory incorporates the U(1) and SU(d) gauge terms of Einstein–Maxwell–Yang–Mills theory, and is invariant under U(1) and SU(d) gauge transformations. The special case where symmetric fields are multiples of the identity matrix closely approximates Einstein–Maxwell–Yang–Mills theory in that the extra terms in the field equations are < 10^?13 of the usual terms for worst-case fields accessible to measurement. The theory contains a symmetric metric and Hermitian vector potential, and is easily coupled to the additional fields of Weinberg–Salam theory or flipped SU(5) GUT theory. We also consider the case where symmetric fields have small traceless parts, and show how this suggests a possible dark matter candidate.     

On Twisted N = 2 5D Super Yang–Mills Theory

On a five-dimensional simply connected Sasaki–Einstein manifold, one can construct Yang–Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however, the contact instanton equations are not elliptic. It turns out that these equations can be embedded into the Haydys–Witten equations (which are elliptic) in the same way the 4D anti-self-dual instanton equations are embedded in the Vafa–Witten equations. We show that under some favourable circumstances, the latter equations will reduce to the former by proving some vanishing theorems. It was also known that the Haydys–Witten equations on product manifolds \({M_5 = M_4 \times \mathbb{R}}\) arise in the context of twisting the 5D maximally supersymmetric Yang–Mills theory. In this paper, we present the construction of twisted N = 2 Yang–Mills theory on Sasaki–Einstein manifolds, and more generally on K-contact manifolds. The localisation locus of this new theory thus provides a covariant version of the Haydys–Witten equation.     

Asymptocic Freedom of Gluons in Hamiltonian Dynamics

We derive asymptotic freedom of gluons in terms of the renormalized SU(3) Yang–Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles to calculate the three-gluon interaction term in the front-form Yang–Mills Hamiltonian using a perturbative expansion in powers of g up to third order. The resulting three-gluon vertex is a function of the scale parameter s that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian \({\beta}\) -function coincides with the one obtained in an earlier calculation using a different generator.     

Generalized Kähler Potentials from Supergravity

We consider supersymmetric \({\mathcal{N} = 2}\) solutions with non–vanishing NS three–form. Building on worldsheet results, we reduce the problem to a single generalized Monge–Ampère equation on the generalized Kähler potential K recently interpreted geometrically by Lindström, Ro?ek, Von Unge and Zabzine. One input in the procedure is a holomorphic function w that can be thought of as the effective superpotential for a D3 brane probe. The procedure is hence likely to be useful for finding gravity duals to field theories with non–vanishing abelian superpotential, such as Leigh–Strassler theories. We indeed show that a purely NS precursor of the Lunin–Maldacena dual to the β–deformed \({\mathcal{N} = 4}\) super–Yang–Mills falls in our class.     

Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.     

On the energy transport velocity in a dissipative medium

An exact definition of the group velocity v _g is proposed for a wave process with arbitrary dispersion relation ω = ω′(k) + iω″(k). For the monochromatic approximation, a limit expression v _g (k) is obtained. A condition under which v _g (k) takes the form of the Kuzelev–Rukhadze expression [1] dω′(k)/dk is found. In the general case, it appears that v _g (k) is defined not only by the dispersion relation ω(k), but also by other elements of the initial problem. As applied to the dissipative medium, it is shown that v _g (k) defines the field energy transfer velocity, and this velocity does not exceed thee light speed in vacuum. An expression for the energy transfer velocity is also obtained for the case where the dispersion relation is given in the form k = k′(ω) + ik″(ω) which corresponds to the boundary problem.     

Kramers–Kronig Relations in Representation of Modulation Polarimetry by an Example of the Transmission Spectra of GaAs Crystal

The increments of the real and imaginary components of the complex refractive index ΔN = Δn–iΔk of a lightly doped GaAs crystal with a donor concentration of ~10¹⁶ cm^–3 have been measured using modulation polarimetry. It is shown that, within this representation, the birefringence and dichroism spectra (Δn(ω) and Δk(ω), respectively) obtained in the transparency window of a sample subjected to probe strain are derivatives of the corresponding functions: Δn(ω) ≈ dn/dω and Δk(ω) ≈ dk/dω. The experimental characteristics and primary dependences n(ω) and k(ω) derived from them by graphical integration are in agreement with the results of other researchers and measurements carried out by independent methods. The results obtained are compared (taking into account the integral (Kramers–Kronig) relations) with the resonance parameters: amplitude and phase in the Drude–Lorenz model. Agreement between the experimental characteristics and theoretical model predictions can be obtained by choosing an appropriate value of resonance damping parameter.     

Low-Temperature Transport Properties of Lanthanum Hexaboride La<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Ce<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>B<Subscript>6</Subscript> Single Crystals

Resistivity (ρ), thermal conductivity (k) and Seebeck coefficient (S) of La_1–xCe_xB₆ single crystals with various concentrations of cerium Ce ions was measured in a wide temperature range 3?300 K. The obtained data were analyzed in the framework of the Coqblin–Shrieffer model. The contributions of scattering of carriers on magnetic ions Ce for all transport parameters ρ(T), k(T), S(T) are revealed. Strong dependence of the magnetic scattering on concentration of the cerium ions are identified. The anomalous behavior of the transport parameters ρ(T), k(T), S(T) in the region near 30 K is attributed to the Δ ~ 30 K splitting of Г₈ level.     

Branches of zero sound excitations in asymmetric nuclear matter: The dependence on density

Results from calculating zero sound excitations in isospin asymmetric nuclear matter are presented. A polarization operator constructed in the random phase approximations is used in the calculations. Three branches of the complex solutions ω_sτ(k), τ = p,n,np are presented. The type of branch depends on that of the considered branch damping. An imaginary part of the solution corresponds to the damping of collective excitations due to mixing with the background of noninteracting (1) proton particle–hole pairs (ω _sp (k)), (2) neutron particle–hole pairs (ω _sn (k)), and (3) both proton and neutron particle–hole pairs (ω _snp (k)). The behavior of the solutions upon variations in density depends on the value of the asymmetry parameter.     

Cluster-enriched Yang–Baxter equation from SUSY gauge theories

We propose a new generalization of the Yang–Baxter equation, where the R-matrix depends on cluster y-variables in addition to the spectral parameters. We point out that we can construct solutions to this new equation from the recently found correspondence between Yang–Baxter equations and supersymmetric gauge theories. The \(S^2\) partition function of a certain 2d \({\mathcal {N}}=(2,2)\) quiver gauge theory gives an R-matrix, whereas its FI parameters can be identified with the cluster y-variables.     

A Savvidy vacuum with center vortices

The one loop SU(2) effective potential of a constant chromomagnetic field and thin vortex has been obtained using the background field method in the scope of the Yang–Mills theory. The possible relationship between a Savvidy vacuum and a spaghetti vacuum is discussed.     

Density functional study of $$\hbox {AgScO}_2$$: Electronic and optical properties

Dielectric relaxation studies of binary (jk) polar mixtures of tetrahydrofuran with N-methyl acetamide, N,N-dimethyl acetamide, N-methyl formamide and N,N-dimethyl formamide dissolved in benzene(i) for different weight fractions (w _{j k} ’s) of the polar solutes and mole fractions (x _j ’s) of tetrahydrofuran at 25 ^°C are attempted by measuring the conductivity of the solution under 9.90 GHz electric field using Debye theory. The estimated relaxation time (τ _{j k} ’s) and dipole moment (μ _{j k} ’s) agree well with the reported values signifying the validity of the proposed methods. Structural and associational aspects are predicted from the plot of τ _{j k} and μ _{j k} against x _j of tetrahydrofuran to arrive at solute–solute (dimer) molecular association upto x _j =0.3 of tetrahydrofuran and thereafter solute–solvent (monomer) molecular association upto x _j =1.0 for all systems except tetrahydrofuran + N,N-dimethyl acetamide.     

Structural features and the microscopic dynamics of the three-component Zr<Subscript>47</Subscript>Cu<Subscript>46</Subscript>Al<Subscript>7</Subscript> system: Equilibrium melt,supercooled melt,and amorphous alloy

The structural and dynamic properties of the three-component Zr₄₇Cu₄₆Al₇ system are subjected to a molecular dynamics simulation in the temperature range T = 250–3000 K at a pressure p = 1.0 bar. The temperature dependences of the Wendt–Abraham parameter and the translation order parameter are used to determine the glass transition temperature in the Zr₄₇Cu₄₆Al₇ system, which is found to be T_c ≈ 750 K. It is found that the bulk amorphous Zr₄₇Cu₄₆Al₇ alloy contains localized regions with an ordered atomic structures. Cluster analysis of configuration simulation data reveals the existence of quasi-icosahedral clusters in amorphous metallic Zr–Cu–Al alloys. The spectral densities of time radial distribution functions of the longitudinal (C?_L(k, ω)) and transverse (C?_T(k, ω)) fluxes are calculated in a wide wavenumber range in order to study the mechanisms of formation of atomic collective excitations in the Zr₄₇Cu₄₆Al₇ system. It was found that a linear combination of three Gaussian functions is sufficient to reproduce the (C?_L(k, ω)) spectra, whereas at least four Gaussian contributions are necessary to exactly describe the (C?_T(k, ω)) spectra of the supercooled melt and the amorphous metallic alloy. It is shown that the collective atomic excitations in the equilibrium melt at T = 3000 K and in the amorphous metallic alloy at T = 250 K are characterized by two dispersion acoustic-like branches related with longitudinal and transverse polarizations.     

Reducible Connections and Non-local Symmetries of the Self-dual Yang–Mills Equations

We construct the most general reducible connection that satisfies the self-dual Yang–Mills equations on a simply-connected, open subset of flat ${\mathbb{R}^4}$ . We show how all such connections lie in the orbit of the flat connection on ${\mathbb{R}^4}$ under the action of non-local symmetries of the self-dual Yang–Mills equations. Such connections fit naturally inside a larger class of solutions to the self-dual Yang–Mills equations that are analogous to harmonic maps of finite type.     

A New Model in the Calogero–Ruijsenaars Family

Hamiltonian reduction is used to project a trivially integrable system on the Heisenberg double of SU(n, n), to obtain a system of Ruijsenaars type on a suitable quotient space. This system possesses BC _n symmetry and is shown to be equivalent to the standard three-parameter BC _n hyperbolic Sutherland model in the cotangent bundle limit.     

Oxidation of Self-Duality to 12 Dimensions and Beyond

Using (partial) curvature flows and the transitive action of subgroups of ${{\rm O}(d, \mathbb{Z})}$ on the indices ${\{1, \ldots,d \}}$ of the components of the Yang–Mills curvature in an orthonormal basis, we obtain a nested system of equations in successively higher dimensions d, each implying the Yang–Mills equations on d-dimensional Riemannian manifolds possessing special geometric structures. This ‘matryoshka’ of self-duality equations contains the familiar self-duality equations on Riemannian fourfold as well as their generalisations on complex Kähler threefold and on seven- and eight-dimensional manifolds with G₂ and Spin(7) holonomy. The matryoshka allows enlargement (‘oxidation’) to a remarkable system in 12 dimensions, invariant under Sp(3). There are hints that the underlying geometry is related to the sextonions, a six-dimensional algebra between the quaternions and octonions.     

Seiberg–Witten theory as a Fermi gas

We explore a new connection between Seiberg–Witten theory and quantum statistical systems by relating the dual partition function of SU(2) Super Yang–Mills theory in a self-dual \(\Omega \) background to the spectral determinant of an ideal Fermi gas. We show that the spectrum of this gas is encoded in the zeroes of the Painlevé \(\mathrm{III}_3\) \(\tau \) function. In addition, we find that the Nekrasov partition function on this background can be expressed as an O(2) matrix model. Our construction arises as a four-dimensional limit of a recently proposed conjecture relating topological strings and spectral theory. In this limit, we provide a mathematical proof of the conjecture for the local \({\mathbb P}^1 \times {\mathbb P}^1\) geometry.