Simplified TBA equations of the AdS_5 x S^5 mirror model
Gleb Arutyunov, Sergey Frolov
TL;DR
This work streamlines the finite-size spectral analysis of the AdS5×S5 mirror model by applying a canonical TBA reduction with the operator $(K+1)$ and leveraging a new integral representation for the dressing phase. It eliminates slow-converging infinite sums over string sectors, recasts the $Q$-particle dressing contribution into a simple kernel form, and provides explicit integral representations to enable efficient analytic and numerical study. The results yield a compact, practical set of simplified TBA equations, including a computable dressing-kernel $\check K^\Sigma_Q$, applicable to ground and potentially excited states. Overall, the methods deliver a more tractable starting point for exploring the finite-size spectrum in the AdS/CFT context.
Abstract
We use the recently found integral representation for the dressing phase in the kinematic region of the mirror theory to simplify the TBA equations for the AdS_5 x S^5 mirror model. The resulting set of equations provides an efficient starting point for both analytic and numerical studies.