Exact S-matrices for AdS_3/CFT_2

TL;DR

This paper derives exact two-particle S-matrices for the AdS_3/CFT_2 duality, confirming the all-loop Bethe ansatz and providing a key step in understanding the integrable structure of these theories.

Contribution

It presents the complete two-particle S-matrices for AdS_3/CFT_2 duality, based on symmetry considerations and matching with the all-loop Bethe ansatz.

Findings

Derived exact two-particle S-matrices for AdS_3/CFT_2.

Confirmed the all-loop Bethe ansatz matches the proposed S-matrices.

Provided symmetry-based justification for the integrability of the duality.

Abstract

We propose exact $S$-matrices for the AdS_3/CFT_2 duality between Type IIB strings on AdS_3 x S^3 x M_4 with M_4=S^3 x S^1 or T^4 and the corresponding two-dimensional conformal field theories. We fix the complete two-particle S-matrices for both those cases of AdS_3/CFT_2, on the basis of the symmetries su(1|1) and su(1|1) x su(1|1), respectively preserved by their vacua. A crucial justification comes from the derivation of the all-loop Bethe ansatz matching exactly the recent conjecture proposed by [1] and [2].