One-loop quantization of rigid spinning strings in $AdS_3 \times S^3 \times T^4$ with mixed flux

TL;DR

This paper calculates the one-loop quantum corrections to spinning string solutions in a complex background with mixed fluxes, revealing that corrections vanish in the pure NS-NS flux limit, and employs two different methods for the analysis.

Contribution

It introduces a detailed one-loop correction computation for rigid spinning strings in $AdS_3 imes S^3 imes T^4$ with mixed fluxes, utilizing both fluctuation analysis and integrability techniques.

Findings

One-loop correction vanishes in the pure NS-NS limit.

Two methods confirm the correction results.

Extension to arbitrary angular momenta in the NS-NS limit.

Abstract

We compute the one-loop correction to the classical dispersion relation of rigid closed spinning strings with two equal angular momenta in the $AdS_3 \times S^3 \times T^4$ background supported with a mixture of R-R and NS-NS three-form fluxes. This analysis is extended to the case of two arbitrary angular momenta in the pure NS-NS limit. We perform this computation by means of two different methods. The first method relies on the Euler-Lagrange equations for the quadratic fluctuations around the classical solution, while the second one exploits the underlying integrability of the problem through the finite-gap equations. We find that the one-loop correction vanishes in the pure NS-NS limit.