Two-Dimensional Instantons with Bosonization and Physics of Adjoint $QCD_2$
| dc.creator | Smilga, A. V. | |
| dc.date | 1996-07-01 | |
| dc.date | 1996-07-08 | |
| dc.date.accessioned | 2026-07-07T12:03:50Z | |
| dc.date.available | 2026-07-07T12:03:50Z | |
| dc.description | 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 $N \geq 4$. | |
| dc.description | 36 pages, LaTeX. References added | |
| dc.identifier | https://arxiv.org/abs/hep-th/9607007 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9607007 | |
| dc.identifier | Phys.Rev.D54:7757-7773,1996 | |
| dc.identifier | doi:10.1103/PhysRevD.54.7757 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/207929 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Two-Dimensional Instantons with Bosonization and Physics of Adjoint $QCD_2$ | |
| dc.type | text |