Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2

TL;DR

This paper introduces a novel method to derive quantum spectral curves for AdS/CFT systems by analyzing algebraic automorphisms, leading to new curves that connect to the Hubbard model and AdS3/CFT2 backgrounds.

Contribution

It develops a procedure to derive quantum spectral curves via analytic continuation and automorphisms, resulting in four new curves including those related to the Hubbard model and AdS3/CFT2.

Findings

Derived four new quantum spectral curves based on SU(2|2) and SU(2|2) x SU(2|2) symmetries.

Connected one of the curves to the Hubbard model under specific assumptions.

Supported the AdS3/CFT2 conjecture by verifying consistency with Bethe equations.

Abstract

We propose a procedure to derive quantum spectral curves of AdS/CFT type by requiring that a specially designed analytic continuation around the branch point results in an automorphism of the underlying algebraic structure. In this way we derive four new curves. Two are based on SU(2|2) symmetry, and we show that one of them, under the assumption of square root branch points, describes Hubbard model. Two more are based on SU(2|2) x SU(2|2). In the special subcase of zero central charge, they both reduce to the unique nontrivial curve which furthermore has analytic properties compatible with PSU(1,1|2) x PSU(1,1|2) real form. A natural conjecture follows that this is the quantum spectral curve of AdS/CFT integrable system with AdS3 x S3 x T4 background supported by RR-flux. We support the conjecture by verifying its consistency with the massive sector of asymptotic Bethe equations in the large volume regime. For this spectral curve, it is compulsory that branch points are not of the square root type which qualitatively distinguishes it from the previously known cases.