Searcharxiv⌕ Search

arXiv subjects

A. V. Smilga

Publications and source records attributed to A. V. Smilga.

At least 73 records · Page 4Linked to original sources
arXiv1999

Normalized Vacuum States in N = 4 Supersymmetric Yang--Mills Quantum Mechanics with Any Gauge Group

We study the question of existence and the number of normalized vacuum states in N = 4 super-Yang-Mills quantum mechanics for any gauge group. The mass deformation method is the simplest and clearest one. It allowed us to calculate the number of normalized vacuum states for all gauge groups. For all unitary groups, #(vac) = 1, but for the symplectic groups [starting from Sp(6) ], for the orthogonal groups [starting from SO(8)] and for all the exceptional groups, it is greater than one. We also discuss at length the functional integral method. We calculate the ``deficit term'' for some non-unitary groups and predict the value of the integral giving the ``principal contribution''. The issues like the Born-Oppenheimer procedure to derive the effective theory and the manifestation of the localized vacua for the asymptotic effective wave functions are also discussed.

hep-th↗
arXiv1999

Vacuum structure in supersymmetric Yang-Mills theories with any gauge group

We consider the pure supersymmetric Yang--Mills theories placed on a small 3-dimensional spatial torus with higher orthogonal and exceptional gauge groups. The problem of constructing the quantum vacuum states is reduced to a pure mathematical problem of classifying the flat connections on 3-torus. The latter problem is equivalent to the problem of classification of commuting triples of elements in a connected simply connected compact Lie group which is solved in this paper. In particular, we show that for higher orthogonal SO(N), N > 6, and for all exceptional groups the moduli space of flat connections involves several distinct connected components. The total number of vacuumstates is given in all cases by the dual Coxeter number of the group which agrees with the result obtained earlier with the instanton technique.

hep-th↗
arXiv1999

Physics of hot and dense QCD

We give a brief review of modern theoretical understanding of the physics of QCD at finite temperature and density. We concentrate in particular on the properties of hadron gas at relatively small temperatures and discuss in details the physics of the phase transition. We argue that the phase transition in temperature is probably absent, but it can appear with a vengeance when finite density effects are taken into account. We notice also that the temperatures one can expect to reach at the heavy ion collider at RHIC are not yet high enough for the perturbation theory in the QCD coupling constant to work well.

hep-ph↗
arXiv1998

BPS and non-BPS domain walls in supersymmetric QCD

We study the spectrum of the domain walls interpolating between different chirally asymmetric vacua in supersymmetric QCD with the SU(N) gauge group and including N-1 pairs of chiral matter multiplets in fundamental and anti-fundamental representations. There are always "real walls" interpolating between the chirally symmetric and a chirally asymmetric vacua which are BPS saturated. For small enough masses, there are two different "complex" BPS wall solutions interpolating between different chirally asymmetric vacua and two types of "wallsome sphalerons". At some m = m_*, two BPS branches join together and, in some interval m_* < m < m_{**}, BPS equations have no solutions, but there are solutions to the equations of motion describing a non--BPS domain wall and a sphaleron. For m > m_{**}, there are no complex wall solutions whatsoever.

hep-th↗
arXiv1998

Electron Self-Energy in Strong Magnetic Field: Summation of Double Logarithmic Terms

We study the electron self--energy in a strong magnetic field when the parameter η\equiv (α/2π) \ln^2 (eB/m^2_0) \sim 1 and explore the transition between the perturbative regime η<<1 and the nonperturbative massless QED regime η>>1 where chiral symmetry is broken spontaneously and electrons acquire the dynamically induced mass.

hep-ph↗
arXiv1998

QCD at θ\sim π

Taking into account the quadratic in mass terms in the effective chiral lagrangian, we show that, at θ\sim π, the theory with 2 light quarks of equal mass involves two degenerate vacuum states separated by a barrier. For three flavors, the energy barrier between two vacua appears already in the leading order in mass. This corresponds to the first order phase transition at θ= π. The surface energy density of the domain wall separating two different vacua is calculated. In the immediate vicinity of the phase transition point, two minima of the potential still exist, but one of them becomes metastable. The probability of the false vacuum decay is estimated.

hep-ph↗
arXiv1998

Isolated vacua in supersymmetric Yang-Mills theories

An explicit proof of the existence of nontrivial vacua in the pure supersymmetric Yang-Mills theories with higher orthogonal SO(N), N>=7 or the G_2 gauge group defined on a 3-torus with periodic boundary conditions is given. Extra vacuum states are separated by an energy barrier from the perturbative vacuum A_i=0 and its gauge copies.

hep-th↗
arXiv1998

BPS and non-BPS Domain Walls in Supersymmetric QCD with SU(3) Gauge Group

We study the spectrum of the domain walls interpolating between different chirally asymmetric vacua in supersymmetric QCD with the SU(3) gauge group and including 2 pairs of chiral matter multiplets in fundamental and anti-fundamental representations. For small enough masses m < m* = .286... (in the units of Λ), there are two different domain wall solutions which are BPS-saturated and two types of ``wallsome sphalerons''. At m = m*, two BPS branches join together and, in the interval m* < m < m** = 3.704..., BPS equations have no solutions but there are solutions to the equations of motion describing a non-BPS domain wall and a sphaleron. For m > m**, there are no solutions whatsoever.

hep-th↗
arXiv1998

6 + 1 Vacua in Supersymmetric QCD with G_2 Gauge Group

We consider N=1 supersymmetric QCD based on the G_2 gauge group and including 3 chiral matter 7-plets. In that case, the gauge symmetry is broken completely and the instanton-generated superpotential on the classical moduli space is present. If the theory involves the Yukawa term, there are six chirally asymmetric vacua. In the limit when the Yukawa coupling vanishes, two of the vacua run away to infinity and only 4 asymmetric vacuum states are left. Besides, a chirally symmetric state is always present. We consider also an O(7) model with 4 chiral multiplets in spinor representation. In that case, there are 4 extra "virtual vacua" dwelling at infinity of the moduli space. In a non-renormalizable theory involving a quartic term in the superpotential, they show up at finite moduli values.

hep-th↗
arXiv1997

Domain Walls Zoo in Supersymmetric QCD

Solving numerically the equations of motion for the effective lagrangian describing supersymmetric QCD with the SU(2) gauge group, we find a menagerie of complex domain wall solutions connecting different chirally asymmetric vacua. Some of these solutions are BPS saturated walls; they exist when the mass of the matter fields does not exceed some critical value m < m* < 4.67059... There are also sphaleron branches (saddle points of the ebergy functional). In the range m* < m < m** \approx 4.83, one of these branches becomes a local minimum (which is not a BPS saturated one). At m > m*, the complex walls disappear altogether and only the walls connecting a chirally asymmetric vacuum with the chirally symmetric one survive.

hep-th↗
arXiv1997

Physics of Thermal QCD

We give a review of modern theoretical understanding of the physics of QCD at finite temperature. Three temperature regions are studied in details: the low temperature region where the system presents a rarefied pion gas and its properties are described by chiral perturbation theory, the high temperature region where the system is adequately described in terms of quarks and gluons, and the intermediate region where phase transition occurs in some variants of the theory.

hep-ph↗
arXiv1997

Quark condensate in a magnetic field

We study the dependence of quark condensate $Σ$ on an external magnetic field. For weak fields, it rises linearly with the field. Pion mass and residue are also shifted so that the Gell-Mann - Oakes - Renner relation is satisfied. In the strong field region, $Σ(H) \propto (eH)^{3/2}$.

hep-ph↗
arXiv1996

Critical amplitudes in two-dimensional theories

We derive exact analytical expressions for the critical amplitudes $A_ψ$, $A_{gap}$ in the scaling laws for the fermion condensate $<\bar ψψ> = A_ψm^{1/3} g^{2/3}$ and for the mass of the lightest state $M_{gap} = A_{gap} m^{2/3} g^{1/3}$ in the Schwinger model with two light flavors, $m \ll g$. $A_ψ$ and $A_{gap}$ are expressed via certain universal amplitude ratios being calculated recently in TBA technique and the known coefficient $A_{ψψ}$ in the scaling law $<\bar ψψ(x) \bar ψψ(0)> = A_{ψψ} (g/x)$ at the critical point. Numerically, $A_ψ= -0.388..., A_{gap} = 2.008...$ . The same is done for the standard square lattice Ising model at $T = T_c$. Using recent Fateev's results, we get $<σ_{lat}> = 1.058... (H_{lat}/T_c)^{1/15}$ for the magnetization and $M_{gap} = a/ξ= 4.010... (H_{lat}/T_c)^{8/15}$ for the inverse correlation length ($a$ is the lattice spacing). The theoretical prediction for $<σ^{lat}>$ is in a perfect agreement with numerical data. Two available numerical papers give the values of $M_{gap}$ which differ from each other by a factor $\approx \sqrt{2}$ . The theoretical result for $M_{gap}$ agrees with one of them.

hep-th↗
arXiv1996

Two-Dimensional Instantons with Bosonization and Physics of Adjoint $QCD_2$

We evaluate partition functions $Z_I$ in topologically nontrivial (instanton) gauge sectors in the bosonized version of the Schwinger model and in a gauged WZNW model corresponding to $QCD_2$ with adjoint fermions. We show that the bosonized model is equivalent to the fermion model only if a particular form of the WZNW action with gauge-invariant integrand is chosen. For the exact correspondence, it is necessary to integrate over the ways the gauge group $SU(N)/Z_N$ is embedded into the full $O(N^2 - 1)$ group for the bosonized matter field. For even $N$, one should also take into account the contributions of both disconnected components in $O(N^2 - 1)$. In that case, $Z_I \propto m^{n_0}$ for small fermion masses where $2n_0$ coincides with the number of fermion zero modes in a particular instanton background. The Taylor expansion of $Z_I/m^{n_0}$ in mass involves only even powers of $m$ as it should. The physics of adjoint $QCD_2$ is discussed. We argue that, for odd $N$, the discrete chiral symmetry $Z_2 \otimes Z_2$ present in the action is broken spontaneously down to $Z_2$ and the fermion condensate $<\barλ λ>_0$ is formed. The system undergoes a first order phase transition at $T_c = 0$ so that the condensate is zero at an arbitrary small temperature. It is not yet quite clear what happens for even $N \geq 4$.

hep-th↗
arXiv1996

Physics of Quark--Gluon Plasma

In this lecture, we give a brief review of what theorists now know, understand, or guess about static and kinetic properties of quark--gluon plasma. A particular attention is payed to the problem of physical observability, i.e. the physical meaningfulness of various characteristics of $QGP$ discussed in the literature.

hep-ph↗
arXiv1995

Screening vs. Confinement in 1+1 Dimensions

We show that, in 1+1 dimensional gauge theories, a heavy probe charge is screened by dynamical massless fermions both in the case when the source and the dynamical fermions belong to the same representation of the gauge group and, unexpectedly, in the case when the representation of the probe charge is smaller than the representation of the massless fermions. Thus, a fractionally charged heavy probe is screened by dynamical fermions of integer charge in the massless Schwinger model, and a colored probe in the fundamental representation is screened in $QCD_2$ with adjoint massless Majorana fermions. The screening disappears and confinement is restored as soon as the dynamical fermions are given a non-zero mass. For small masses, the string tension is given by the product of the light fermion mass and the fermion condensate with a known numerical coefficient. Parallels with 3+1 dimensional $QCD$ and supersymmetric gauge theories are discussed.

hep-th↗
arXiv1994

No $Z_N$ - bubbles in hot Yang-Mills theory

Pure Yang-Mills theory at high temperature is considered. We show that no distinct $Z_N$- phases separated by domain walls do exist in the physical Minkowski space. That means the absense of the spontaneous breaking of $Z_N$- symmetry in the physical meaning of this word.

hep-th↗