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

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.

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