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

dc.creatorSmilga, A. V.
dc.date1996-07-01
dc.date1996-07-08
dc.date.accessioned2026-07-07T12:03:50Z
dc.date.available2026-07-07T12:03:50Z
dc.descriptionWe 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 $N \geq 4$.
dc.description36 pages, LaTeX. References added
dc.identifierhttps://arxiv.org/abs/hep-th/9607007
dc.identifierhttp://arxiv.org/abs/hep-th/9607007
dc.identifierPhys.Rev.D54:7757-7773,1996
dc.identifierdoi:10.1103/PhysRevD.54.7757
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/207929
dc.subjectHigh Energy Physics - Theory
dc.titleTwo-Dimensional Instantons with Bosonization and Physics of Adjoint $QCD_2$
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