More on the Tensor Response of the QCD Vacuum to an External Magnetic Field

TL;DR

This paper explores how an external magnetic field affects the QCD vacuum, revealing a complex interplay between different theoretical components and enabling calculations of magnetic susceptibility to all orders.

Contribution

It demonstrates the implications of the Son-Yamamoto relation in the IR and introduces a holographic approach to compute magnetic susceptibility of the quark condensate.

Findings

IR Son-Yamamoto relation implies interplay between kinetic and WZW terms

External magnetic field causes mixing of scalar and tensor fields in holography

Magnetic susceptibility can be calculated to all orders in magnetic field

Abstract

In this Letter we discuss a few issues concerning the magnetic susceptibility of the quark condensate and the Son-Yamamoto (SY) anomaly matching equation. It is shown that the SY relation in the IR implies a nontrivial interplay between the kinetic and WZW terms in the chiral Lagrangian. It is also demonstrated that in a holographic framework an external magnetic field triggers mixing between scalar and tensor fields. Accounting for this, one may calculate the magnetic susceptibility of the quark condensate to all orders in the magnetic field.