Quantum corrections to minimal surfaces with mixed three-form flux

TL;DR

This paper computes quantum corrections to minimal surfaces in a mixed flux background of AdS3×S3×T4, revealing how flux types influence the conformal anomaly and divergences, and demonstrating consistency with zeta-function regularization.

Contribution

It provides a detailed calculation of quantum corrections to minimal surfaces with mixed flux, including the effects of the B-field and flux regimes, using functional determinants and regularization techniques.

Findings

The B-field contribution is included in the conformal anomaly when RR flux is present.

The Gel'fand-Yaglom and Abel-Plana methods are effectively used for determinant calculations.

Results are consistent with zeta-function regularization and simplify in the pure NS-NS flux limit.

Abstract

We obtain the ratio of semiclassical partition functions for the extension under mixed flux of the minimal surfaces subtending a circumference and a line in Euclidean $AdS_{3}\times S^{3}\times T^{4}$. We reduce the problem to the computation of a set of functional determinants. If the Ramond-Ramond flux does not vanish, we find that the contribution of the $B$-field is comprised in the conformal anomaly. In this case, we successively apply the Gel'fand-Yaglom method and the Abel-Plana formula to the flat-measure determinants. To cancel the resultant infrared divergences, we shift the regularization of the sum over half-integers depending on whether it corresponds to massive or massless fermionic modes. We show that the result is compatible with the zeta-function regularization approach. In the limit of pure Neveu-Schwarz-Neveu-Schwarz flux we argue that the computation trivializes. We extend the reasoning to other surfaces with the same behavior in this regime.