Weyl Anomaly induced Fermi Condensation and Holography

TL;DR

This paper explores how Weyl anomaly induces Fermi condensation in boundary conformal field theories, generalizing previous results, deriving new formulas, and verifying them through free BCFT and holographic models.

Contribution

It provides generalized expressions for Weyl anomaly and Fermi condensation in 4d BCFTs, extending prior work to more general scalar and pseudo-scalar backgrounds.

Findings

Fermi condensation can be non-zero without background scalar fields.

Derived general formulas for Weyl anomaly in 4d BCFTs with scalar and pseudo-scalar fields.

Validated results using free BCFT and holographic BCFT models.

Abstract

Recently it is found that, due to Weyl anomaly, a background scalar field induces a non-trivial Fermi condensation for theories with Yukawa couplings. For simplicity, the paper consider only scalar type Yukawa coupling and, in the BCFT case, only for a specific boundary condition. In these cases, the Weyl anomaly takes on a simple special form. In this paper, we generalize the results to more general situations. First, we obtain general expressions of Weyl anomaly due to a background scalar and pseudo scalar field in general 4d BCFTs. Then, we derive the general form of Fermi condensation from the Weyl anomaly. It is remarkable that, in general, Fermi condensation is non-zero even if there was not a non-vanishing scalar field background. Finally, we verify our results with free BCFT with Yukawa coupling to scalar and pseudo-scalar background potential with general chiral bag boundary condition and with holographic BCFT. In particular, we obtain the shape and curvature dependence of the Fermi condensate from the holographic one point function.