Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)

Abstract

We analyze the vacuum structure of SU(2) QCD with multiple massless adjoint representation fermions formulated on a small spatial $S^1 \times \R^3$. The absence of thermal fluctuations, and the fact that quantum fluctuations favoring the vacuum with unbroken center symmetry in a weakly coupled regime renders the interesting dynamics of these theories analytically calculable. Confinement, the area law behavior for large Wilson loops, and the generation of the mass gap in the gluonic sector are shown analytically. By abelian duality transformation, the long distance effective theory of QCD is mapped into an amalgamation of $d=3$ dimensional Sine-Gordon and NJL models. The duality necessitates going to IR first. In this regime, theory exhibits confinement without continuous chiral symmetry breaking. However, a flavor singlet chiral condensate (which breaks a discrete chiral symmetry) persists at arbitrarily small $S^1$. Under the reasonable assumption that the theory on $\R^4$ exhibits chiral symmetry breaking, there must exist a zero temperature chiral phase transition in the absence of any change in spatial center symmetry realizations.Comment: 4 page