Bound states in the mirror TBA

Abstract

AbstractThe spectrum of the light-cone AdS5×S5superstring contains states composed of particles with complex momenta including in particular those which turn into bound states in the decompactification limit. We propose the mirror TBA description for these states. We focus on a three-particle state which is a finite-size representative of a scattering state of a fundamental particle and a two-particle bound state and dual to an operator from the$ \mathfrak{s}\mathfrak{u}(2) $sector of$ \mathcal{N} = 4\;{\text{SYM}} $. We find that the analytic behavior of Y-functions differs drastically from the case of states with real momenta. Most importantly,YQ-functions exhibit poles in the analyticity strip which leads to the appearance of new terms in the formula for the energy of this state. In addition, the TBA equations are supplied by quantization conditions which involveY2. Considering yet another example of a three- particle state, we find that the corresponding quantization conditions do not even involveY1. Our treatment can be generalized to a wide class of states with complex momenta.