TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT

TL;DR

This paper derives and compares NLO Luscher corrections and TBA equations for twisted integrable theories, providing explicit finite-size energy results including double-wrapping effects in deformed AdS/CFT models.

Contribution

It introduces a consistent framework for calculating NLO finite-volume corrections in twisted integrable theories, including explicit double-wrapping corrections in AdS/CFT.

Findings

Derived NLO Luscher corrections for twisted theories.

Established agreement between Luscher and TBA approaches at NLO.

Explicit six-loop double-wrapping correction in the γ-deformed AdS/CFT model.

Abstract

The ground-state energy of integrably-twisted theories is analyzed in finite volume. We derive the leading and next-to-leading order (NLO) L\"uscher-type corrections for large volumes of the vacuum energy for integrable theories with twisted boundary conditions and twisted S-matrix. We then derive the twisted thermodynamic Bethe ansatz (TBA) equations to describe exactly the ground state, from which we obtain an untwisted Y-system. The two approaches are compared by expanding the TBA equations to NLO, and exact agreement is found. We give explicit results for the O(4) model and for the three-parameter family of $\gamma$-deformed (non-supersymmetric) planar AdS/CFT model, where the ground-state energy can be nontrivial and can acquire finite-size corrections. The NLO corrections, which correspond to double-wrapping diagrams, are explicitly evaluated for the latter model at six loops.