TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
Changrim Ahn, Zoltan Bajnok, Diego Bombardelli, Rafael I. Nepomechie
TL;DR
This work develops a complete, cross-validated framework for finite-volume ground-state energies in integrable theories with twists. By deriving both LO and NLO Lüscher corrections and twisted TBA equations (with a universal Y-system), it shows exact agreement between the two approaches for the O(4) model and the γ-deformed AdS/CFT theory. The NLO (double-wrapping) corrections are computed explicitly, including a full treatment of the AdS/CFT bound-state spectrum and dressing factors, yielding a six-loop prediction for Tr Z^3 in the twisted theory. The analysis confirms that twists influence the asymptotics but not the local TBA/Y-system structure, and it establishes a solid foundation for extending to excited states and higher-wrapping orders. Overall, the results provide a highly nontrivial consistency check of the integrable S-matrix and the finite-size framework in twisted AdS/CFT.
Abstract
The ground-state energy of integrably-twisted theories is analyzed in finite volume. We derive the leading and next-to-leading order (NLO) Lüscher-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 $γ$-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.