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

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.