Covariant quantization of the superstring in $\rm AdS_3 \times S^3 \times T^4$ with mixed flux

TL;DR

This paper develops a covariant, quantizable superstring action in $ m AdS_3 imes S^3 imes T^4$ with mixed flux, demonstrating its conformal invariance and connecting it to existing models.

Contribution

It constructs a new superstring action with mixed flux in $ m AdS_3 imes S^3 imes T^4$ that is manifestly invariant and quantizable, extending previous pure spinor formulations.

Findings

Successfully quantized the superstring model.

Proved conformal invariance at one-loop level.

Connected the model to existing worldsheet actions.

Abstract

A quantizable and manifestly $\text{PSU}(1,1|2) \times \text{PSU}(1,1|2)$-invariant action for the superstring in $\rm AdS_3 \times S^3 \times T^4$ with mixed NS-NS and R-R self-dual three-form flux is constructed, which is the analogue of the $\rm AdS_5 \times S^ 5$ pure spinor action for $\rm AdS_3 \times S^3$. The model is then quantized and proven to be conformal invariant at the one-loop level. We conclude by showing how one can relate the supersymmetric description with the Berkovits-Vafa-Witten $\rm AdS_3 \times S^3$ worldsheet action with mixed flux.