Two-dimensional instantons with bosonization and physics of adjoint two-dimensional QCD

Journal Article · Sun Dec 01 04:00:00 EST 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.54.7757· OSTI ID:399929

Smilga, A V ^[1]

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1. Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya 25, Moscow 117259 (Russia)

We evaluate partition functions {ital Z}{sub {ital I}} in topologically nontrivial (instanton) gauge sectors in the bosonized version of the Schwinger model and in a gauged WZNW model corresponding to two-dimensional QCD (QCD{sub 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 a gauge-invariant integrand is chosen. For the exact correspondence, it is necessary to integrate over the ways the gauge group SU({ital N})/{ital Z}{sub {ital N}} is embedded into the full O({ital N}{sup 2}{minus}1) group for the bosonized matter field. For even {ital N}, one should also take into account the contributions of both disconnected components in O({ital N}{sup 2}{minus}1). In that case, {ital Z}{sub {ital I}}{proportional_to}{ital m}{sup {ital n}{sub 0}} for small fermion masses where 2{ital n}{sub 0} coincides with the number of fermion zero modes in a particular instanton background. The Taylor expansion of {ital Z}{sub {ital I}}/{ital m}{sup {ital n}{sub 0}} in mass involves only even powers of {ital m}, as it should. The physics of adjoint QCD{sub 2} is discussed. We argue that, for odd {ital N}, the discrete chiral symmetry {ital Z}{sub 2}{circle_times}{ital Z}{sub 2} present in the action is broken spontaneously down to {ital Z}{sub 2} and the fermion condensate {l_angle}{bar {lambda}}{lambda}{r_angle}{sub 0} is formed. The system undergoes a first order phase transition at {ital T}{sub {ital c}}=0 so that the condensate is zero at an arbitrary small temperature. It is not yet quite clear what happens for even {ital N}{ge}4. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 399929
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 12 Vol. 54; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOSONS
FERMIONS
GAUGE INVARIANCE
INSTANTONS
MATTER
PARTITION FUNCTIONS
QUANTUM CHROMODYNAMICS
SU GROUPS
TWO-DIMENSIONAL CALCULATIONS