Gauge Theories in a Bag

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 $QE{D}_2$ and the abelian projection of $QC{D}_2$. 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 $QC{D}_2$ decreases with increasing bag radius $R$ at least as $\sim R^{-1/N_c{N}_f}$. Finally we determine the correlators of mesonic currents in $QC{D}_2$.

40 pages, LATEX-file

References in corpus (7)

• Gauge Theories in a Bag
• Functional Integral Approach to the N-Flavor Schwinger Model
• Finite Size Effects from General Covariance and Weyl Anomaly
• Fractons in Twisted Multiflavor Schwinger Model
• Temperature- and Curvature Dependence of the Chiral Symmetry Breaking in 2D Gauge Theories
• Conformal- and Thermodynamic Properties of a Family of Thirring-like Models
• How well do lattice simulations reproduce the different aspects of the geometric Schwinger model

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