Green's temperature functions of massive scalar particles for finite matter density

An explicit expression is obtained for the Green's functions of a massive scalar field for nonnull temperatures and density in the form of a series in powers of m/T. The equivalence of the spectral-geometric approach and the temperature technique of Matsubara and Bernard is demonstrated. Corrections to the Stefan-Boltzmann law are obtained on the basis of the calculated Green's functions. The energy density is calculated in regions of high and low temperatures. The formulas obtained can prove to be useful in the discussion of the phase transition hadrons-quark-gluon plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 32–40, July, 1991.     

Singleton Field Theory and Flato–Frønsdal Dipole Equation

We study solutions of the equations ( - ) = 0 and ( - )² = 0 in global coordinates on the covering space CAdS _d of the d-dimensional Anti de-Sitter space subject to various boundary conditions and their connection to the unitary irreducible representations of (d-1,2). The vanishing flux boundary conditions at spatial infinity lead to the standard quantization scheme for CAdS _d in which solutions of the second- and the fourth-order equations are equivalent. To include fields realizing the singleton unitary representation in the bulk of CAdS _d one has to relax the boundary conditions thus allowing for the nontrivial space of solutions of the dipole equation known as the Gupta–Bleuler triplet. We obtain explicit expressions for the modes of the Gupta–Bleuler triplet and the corresponding two-point function. To avoid negative-energy states one must also introduce an additional constraint in the space of solutions of the dipole equation.     

Quasiaccurately solvable quantum mechanics problems and the anharmonic oscillator problem

The basic methods of obtaining the anharmonic oscillator spectrum are briefly reviewed. An approach is discussed to this problem from the point of view of one of the quasiaccurately solvable models of quantum mechanics, whose wave functions are applicable to the construction of a regular perturbation theory. Results are presented of numerical calculations of the ground state energy. Analytic calculations are provided of integrals of the form , occurring in applications of the method of quasiaccurately solvable problems. M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 76–88, February, 1993.     

Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma

Using the anti-de Sitter/conformal field theory correspondence, we relate the shear viscosity eta of the finite-temperature N = 4 supersymmetric Yang-Mills theory in the large N, strong-coupling regime with the absorption cross section of low-energy gravitons by a near-extremal black three-brane. We show that in the limit of zero frequency this cross section coincides with the area of the horizon. From this result we find eta = pi / 8N(2)T3. We conjecture that for finite 't Hooft coupling g(2)(YM)N the shear viscosity is eta = f(g(2)(YM)N)N2T3, where f(x) is a monotonic function that decreases from O(x(-2)ln(-1)(1/x)) at small x to pi/8 when x-->infinity.     

Quasinormal spectrum and the black hole membrane paradigm

The membrane paradigm approach to black hole physics introduces the notion of a stretched horizon as a fictitious time-like surface endowed with physical characteristics such as entropy, viscosity and electrical conductivity. We show that certain properties of the stretched horizons are encoded in the quasinormal spectrum of black holes. We compute analytically the lowest quasinormal frequency of a vector-type perturbation for a generic black hole with a translationally invariant horizon (black brane) in terms of the background metric components. The resulting dispersion relation is identical to the one obtained in the membrane paradigm treatment of the diffusion on stretched horizons. Combined with the Buchel–Liu universality theorem for the membrane's diffusion coefficient, our result means that in the long wavelength limit the black brane spectrum of gravitational perturbations exhibits a universal, purely imaginary quasinormal frequency. In the context of gauge–gravity duality, this provides yet another (third) proof of the universality of shear viscosity to entropy density ratio in theories with gravity duals.     

Vacuum polarization due to a non-Abelian spherically symmetric chromodynamic field at a finite temperature

The model for gluon condensate of the form A _i ^a = _i ^a , A ₀ ^a =0, = const is considered at finite temperatures. The thermodynamic potential is computed in the one-loop approximation. Unlike the zero temperature case, it has a minimum at a nonvanishing condensate field.M. V. Lomonosov State University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 65–71, November, 1992.