Gauge Theories in a Bag

TL;DR

This paper studies multi-flavour gauge theories confined in Euclidean bags, analyzing boundary conditions, symmetry breaking, and condensate formation, with applications to $QED_2$ and $QCD_2$, revealing how condensates depend on parameters like bag radius and number of colours.

Contribution

It introduces a detailed analysis of boundary conditions and $ heta$-dependence in multi-flavour gauge theories confined in bags, including new results on condensate behavior and correlators in $QED_2$ and $QCD_2$.

Findings

A $CP$-breaking $ heta$-term is generated dynamically.

Condensate in $QCD_2$ decreases with bag radius as $ o R^{-1/N_cN_f}$.

Correlators of mesonic currents in $QCD_2$ are determined.

Abstract

We investigate multi-flavour gauge theories confined in $d\es 2n$-dimensional Euclidean bags. The boundary conditions for the 'quarks' break the axial flavour symmetry and depend on a parameter $\theta$. We determine the $\theta$-dependence of the fermionic correlators and determinants and find that a $CP$-breaking $\theta$-term is generated dynamically. As an application we calculate the chiral condensate in multi-flavour $QED_2$ and the abelian projection of $QCD_2$. In the second model a condensate is generated in the limit where the number of colours, $N_c$, tends to infinity. We prove that the condensate in $QCD_2$ decreases with increasing bag radius $R$ at least as $\sim R^{-1/N_cN_f}$. Finally we determine the correlators of mesonic currents in $QCD_2$.