Abstract
We consider various integrable two-parameter deformations of the AdS3 × S3 × T4 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 AdS5 × S5 S matrix in the one parameter deformation limit. Finally, we show that the fermionic q-deformed AdS5 × S5 S matrix also satisfies such a relation.
Highlights
Quantum (q) deformed algebras — referred to as η deformations
We 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 AdS5 × S5 S matrix in the one parameter deformation limit
In general these backgrounds only satisfy a set of generalized supergravity equations [12], which derive from kappa symmetry [13]
Summary
We would like to compute the tree-level two-body worldsheet S matrix of the massive excitations of various inhomogeneous deformations of the AdS3 × S3 × T4 string in the light-cone gauge. We need the corresponding action for each deformation in the light-cone gauge, expanded to quartic order in the fields. In our previous paper [31] we determined this expanded action for deformations of AdS5 × S5. The two-parameter inhomogeneous deformations of AdS3 × S3 × T4 that we are considering, share the metric and B field [28]. Q (ρ, r) = 1 − κ2+ρ2r2 + κ2− 1 + ρ2r2 The second of these backgrounds is manifestly compatible with mirror duality for the one-parameter deformation κ+ = κ, κ− = 0. The remaining (generalized supergravity) backgrounds we consider are given in appendix A
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