Flavoured Large N Gauge Theory in an External Magnetic Field

TL;DR

This paper investigates how an external magnetic field affects a large N gauge theory with fundamental matter, revealing spontaneous chiral symmetry breaking, meson spectrum modifications, and Goldstone boson behavior.

Contribution

It introduces a holographic model with a D7-brane in a magnetic field, demonstrating spontaneous chiral symmetry breaking and analyzing meson spectra in this setup.

Findings

Chiral symmetry is spontaneously broken at zero quark mass.

Zeeman splitting observed in meson spectrum under magnetic field.

Goldstone boson exhibits rac{rac{1}{2}}{m_q} dependence.

Abstract

We consider a D7-brane probe of AdS$_{5}\times S^5$ in the presence of pure gauge $B$-field. In the dual gauge theory, the $B$-field couples to the fundamental matter introduced by the D7-brane and acts as an external magnetic field. The $B$-field supports a 6-form Ramond-Ramond potential on the D7-branes world volume that breaks the supersymmetry and enables the dual gauge theory to develop a non-zero fermionic condensate. We explore the dependence of the fermionic condensate on the bare quark mass $m_{q}$ and show that at zero bare quark mass a chiral symmetry is spontaneously broken. A study of the meson spectrum reveals a coupling between the vector and scalar modes, and in the limit of weak magnetic field we observe Zeeman splitting of the states. We also observe the characteristic $\sqrt{m_{q}}$ dependence of the ground state corresponding to the Goldstone boson of spontaneously broken chiral symmetry.