GMOR relation for a QCD-like theory from S-duality

TL;DR

This paper uses S-duality in a string theory setup to study a QCD-like gauge theory, deriving the GMOR relation for pions and exploring confinement and symmetry breaking.

Contribution

It extends previous work by adding quark masses and deriving the GMOR relation from the dual magnetic theory in a non-supersymmetric string framework.

Findings

Derived the GMOR relation for pions using the magnetic dual theory.

Provided a string theory realization of confinement and chiral symmetry breaking.

Extended the duality approach to include massive quarks in a QCD-like model.

Abstract

Following [1] we study a QCD-like gauge theory using a non-supersymmetric setup in type IIB string theory. The setup includes an $O3$ plane and $N$ D3 anti-branes and it realises a $USp(2N)$ 'electric' gauge theory with four "quarks" in the two-index antisymmetric representation and six heavy scalars in the adjoint representation. Using S-duality we obtain a dual 'magnetic' theory that includes $SO(2N-1)$ gauge theory theory with six scalars in the adjoint representation and four heavy "quarks" in the two-index symmetric representation. The dual theory provides a description of confinement and dynamical symmetry breaking of the form $SU(4)\rightarrow SO(4)$. We extend the results of [1] by adding masses to the quarks in the electric side and deriving parts of the chiral Lagrangian using the dual magnetic theory. In particular, we derive the Gell-Mann-Oakes-Renner (GMOR) relation for Nambu-Goldstone bosons (pions) using the magnetic theory.