Chern-Simons 5-form and Holographic Baryons

TL;DR

This paper proposes a well-defined Chern-Simons term formulation in holographic QCD models, resolving ambiguities for baryon configurations and ensuring correct baryon spectrum constraints and chiral anomaly reproduction.

Contribution

It introduces a new formulation of the Chern-Simons term that correctly handles topologically non-trivial gauge bundles with baryons in holographic QCD models.

Findings

The new Chern-Simons formulation reproduces the correct baryon spectrum constraints.

It ensures the proper realization of the chiral anomaly in the model.

The approach resolves previous ambiguities in defining the Chern-Simons term for baryonic configurations.

Abstract

In the top-down holographic model of QCD based on D4/D8-branes in type IIA string theory and some of the bottom up models, the low energy effective theory of mesons is described by a 5 dimensional Yang-Mills-Chern-Simons theory in a certain curved background with two boundaries. The 5 dimensional Chern-Simons term plays a crucial role to reproduce the correct chiral anomaly in 4 dimensional massless QCD. However, there are some subtle ambiguities in the definition of the Chern-Simons term for the cases with topologically non-trivial gauge bundles, which include the configurations with baryons. In particular, for the cases with three flavors, it was pointed out by Hata and Murata that the naive Chern-Simons term does not lead to an important constraint on the baryon spectrum, which is needed to pick out the correct baryon spectrum observed in nature. In this paper, we propose a formulation of well-defined Chern-Simons term which can be used for the cases with baryons, and show that it recovers the correct baryon constraint as well as the chiral anomaly in QCD.