On quantum deformations of $AdS_3 \times S^3 \times T^4$ and mirror duality

TL;DR

This paper studies integrable two-parameter quantum deformations of the $AdS_3 imes S^3 imes T^4$ superstring, deriving their S matrix, and explores their mirror duality properties, revealing a relation similar to the $AdS_5 imes S^5$ case.

Contribution

It constructs the two-parameter quantum-deformed S matrix for $AdS_3 imes S^3 imes T^4$ superstrings and analyzes its mirror duality, extending known dualities to new deformations.

Findings

Derived the massive tree-level two-body S matrix matching the conjectured $q$-deformed S matrix.

Showed the S matrix satisfies a mirror duality relation under double Wick rotation.

Extended mirror duality properties to fermionic $q$-deformed $AdS_5 imes S^5$ S matrix.

Abstract

We consider various integrable two-parameter deformations of the $AdS_3 \times S^3 \times T^4$ superstring with quantum group symmetry. Working on the string worldsheet in light-cone gauge and to quadratic order in fermions, we obtain their common massive tree-level two-body S matrix, which matches the expansion of the conjectured exact $q$-deformed S matrix. We then analyze the behavior of the exact S matrix under mirror transformation -- a double Wick rotation on the worldsheet -- and find that it satisfies a mirror duality relation analogous to the distinguished $q$-deformed $AdS_5 \times S^5$ S matrix in the one parameter deformation limit. Finally, we show that the fermionic $q$-deformed $AdS_5 \times S^5$ S matrix also satisfies such a relation.