Long strings and symmetric product orbifold from the AdS₃Bethe equations

Dipartimento di Fisica e Astronomia, Università degli Studi di Padova - via Marzolo 8, 35131 Padova, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Padova - via Marzolo 8, 35131 Padova, Italy

^(a) alessandro.sfondrini@unipd.it

Received: 9 November 2020
Accepted: 3 December 2020

Abstract

A particularly rich class of integrable systems arises from the AdS/CFT duality. There, the two-dimensional quantum field theory living on the string worldsheet may be understood in terms of a non-relativistic factorized S matrix, and the energy spectrum may be derived by techniques such as the mirror thermodynamic Bethe ansatz or the quantum spectral curve. In the case of AdS₃/CFT₂ without Ramond-Ramond fluxes, the worldhseet theory is a Wess-Zumino-Witten model with continous and discrete representations which, for the lowest allowed level, is dual to the symmetric product orbifold of a free theory. I will show how continuous representations may arise from integrability, and that at the lowest level the Bethe equations yield the symmetric product orbifold partition function on the nose.