arXiv subjects

A. Smilga

Publications and source records attributed to A. Smilga.

9 recordsLinked to original sources

arXiv2018

Generic HKT geometries in the harmonic superspace approach

We explain how a generic HKT geometry can be derived using the language of N = 4 supersymmetric quantum mechanics. To this end, one should consider a Lagrangian involving several (4,4,0) multiplets defined in harmonic superspace and subject to nontrivial harmonic constraints. Conjecturally, this general construction worked out earlier by Delduc and Ivanov gives a complete classification of all HKT geometries. Each such geometry is generated by two different functions (potentials) of a special type that depend on harmonic superfields and on harmonics. Given these two potentials, one can derive the vielbeins, metric, connections and curvatures, but this is not so simple: one should solve rather complicated differential equations. We illustrate the general construction by giving a detailed derivation of the metric for the hyper-Kaehler Taub-NUT manifold. In the generic case, we arrive at an HKT geometry. In this paper, we give a simple proof of this assertion.

hep-th↗

arXiv1997

Domain Walls in Supersymmetric Yang-Mills Theories

We present a detailed analysis of the domain walls in supersymmetric gluodynamics and SQCD. We use the (corrected) Veneziano-Yankielowicz effective Lagrangians to explicitely obtain the wall profiles and check recent results of Dvali and Shifman (Phys. Lett. B396, (1997) 64: (i) the BPS-saturated nature of the walls; (ii) the exact expressions for the wall energy density which depend only on global features of dynamics (the existence of a non-trivial central extension of N=1 superalgebra in the theories which admit wall-like solutions). If supersymmetry is softly broken by the gluino mass, the degeneracy of the distinct vacua is gone, and one can consider the decay rate of the "false" vacuum into the genuine one. We do this calculation in the limit of the small gluino mass. Finally, we comment on the controversy regarding the existence of $N$ distinct chirally asymmetric vacua in SU(N) SUSY gluodynamics.

hep-th↗

arXiv1997

Complex BPS domain walls and phase transition in mass in supersymmetric QCD

We study the domain walls connecting different chirally asymmetric vacua in supersymmetric QCD. We show that BPS - saturated solutions exist only in the limited range of mass. When m exceeds some critical value, the domain wall either ceases to be BPS - saturated or disappears altogether. In any case, the properties of the system are qualitatively changed.

hep-th↗

arXiv1995

Scalar susceptibility in QCD and the multiflavor Schwinger model

We evaluate the leading infrared behavior of the scalar susceptibility in QCD and in the multiflavor Schwinger model for small non-zero quark mass $m$ and/or small nonzero temperature as well as the scalar susceptibility for the finite volume QCD partition function. In QCD, it is determined by one-loop chiral perturbation theory, with the result that the leading infrared singularity behaves as $\sim \log m$ at zero temperature and as $\sim T/\sqrt m$ at finite temperature. In the Schwinger model with several flavors we use exact results for the scalar correlation function. We find that the Schwinger model has a phase transition at $T=0$ with critical exponents that satisfy the standard scaling relations. The singular behavior of this model depends on the number of flavors with a scalar susceptibility that behaves as $\sim m^{-2/(N_f+1)}$. At finite volume $V$ we show that the scalar susceptibility is proportional to $1/m^2V$. Recent lattice calculations of this quantity by Karsch and Laermann are discussed.

hep-ph↗

arXiv1995

Thermal phase transition in QCD

We give a review of modern theoretical understanding of the problem of thermal phase transition in $QCD$. The existence or non-existence of such transition depends on the nature of the gauge group, the number of light quark flavors , and on the value of quark masses. Numerical lattice measurements indicate that the phase transition {\it does} not occur for the experimentally observed values of quark masses.

hep-ph↗

arXiv1995

Chiral symmetry and spectrum of Euclidean Dirac operator in QCD

Some exact relations for the spectral density $ρ(λ)$ of the Euclidean Dirac operator in $QCD$ are derived. They follow directly from the chiral symmetry of the $QCD$ lagrangian with massless quarks. New results are obtained both in thermodynamic limit when the Euclidean volume $V$ is sent to infinity and also in the theory defined in finite volume where the spectrum is discrete and a nontrivial information on $ρ(λ)$ in the region $λ\sim 1/(|<\bar{q}q>_0|V)$ (the characteristic level spacing) can be obtained. These exact results should be confronted with "experimental" numerical simulations on the lattices and in some particular models for $QCD$ vacuum structure and may serve as a nontrivial test of the validity of these simulations.

hep-th↗

arXiv1995

Sphalerons, instantons, and standing waves on $S^3 \otimes R$

We consider pure $SU(2)$ Yang-Mills theory when the space is compactified to a 3-dimensional sphere with finite radius. The Euclidean classical self-dual solutions of the equations of motion (the instantons) and the static finite energy solutions (the sphalerons) which have been found earlier are rewritten in handy physical variables with the gauge condition $A_0 = 0$. Stationary solutions to the equations of motion in the Minkowski space-time (the standing waves) are discussed. We briefly discuss also the theory defined in a flat finite spherical box with rigid boundary conditions and present the numerical solution describing the sphaleron.

hep-th↗

arXiv1994

Fractons in Twisted Multiflavor Schwinger Model

We consider two-dimensional QED with several fermion flavors on a finite spatial circle. A modified version of the model with {\em flavor-dependent} boundary conditions $ψ_p(L) = e^{2πip/ N} ψ_p(0)$, $p = 1, \ldots , N$ is discussed ($N $ is the number of flavors). In this case a non-contactable contour in the space of the gauge fields is {\em not} determined by large gauge transformations. The Euclidean path integral acquires the contribution from the gauge field configurations with fractional topological charge. The configuration with $ν= 1/N$ is responsible for the formation of the fermion condensate $\langle\barψ_p ψ_p\rangle_0$. The condensate dies out as a power of $L^{-1}$ when the length $L$ of the spatial box is sent to infinity. Implications of this result for non-abelian gauge field theories are discussed in brief.

hep-th↗

arXiv1994

Spectral sum rules and finite volume partition function in gauge theories with real and pseudoreal fermions

Based on the chiral symmetry breaking pattern and the corresponding low-energy effective lagrangian, we determine the fermion mass dependence of the partition function and derive sum rules for eigenvalues of the QCD Dirac operator in finite Euclidean volume. Results are given for $N_c = 2$ and for Yang-Mills theory coupled to several light adjoint Majorana fermions. They coincide with those derived earlier in the framework of random matrix theory.

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