Criticality, Scaling and Chiral Symmetry Breaking in External Magnetic Field

TL;DR

This paper investigates how an external magnetic field influences chiral symmetry breaking and critical phenomena in a holographic gauge theory, revealing self-similar structures and calculating critical exponents.

Contribution

It introduces a holographic model with a D7-brane in a magnetic field to analyze chiral symmetry breaking and critical behavior, including spectrum self-similarity and critical exponents.

Findings

Fermionic condensate depends on quark mass and exhibits self-similar behavior.

At zero quark mass, the stable phase shows chiral symmetry breaking.

The meson spectrum near the critical point displays self-similarity and critical exponents.

Abstract

We consider a D7-brane probe of $AdS_{5}\times S^5$ in the presence of pure gauge $B$-field. The dual gauge theory is flavored Yang-Mills theory in external magnetic field. We explore the dependence of the fermionic condensate on the bare quark mass $m_{q}$ and study the discrete self-similar behavior of the theory near the origin of the parametric space. We calculate the critical exponents of the bare quark mass and the fermionic condensate. A study of the meson spectrum supports the expectation based on thermodynamic considerations that at zero bare quark mass the stable phase of the theory is a chiral symmetry breaking one. Our study reveals the self-similar structure of the spectrum near the critical phase of the theory, characterized by zero fermionic condensate and we calculate the corresponding critical exponent of the meson spectrum.