Bound States in the Mirror TBA
arXiv:1111.0564 · doi:10.1007/JHEP02(2012)014
Abstract
The spectrum of the light-cone AdS_5 \times S^5 superstring 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 su(2) sector of N=4 SYM. We find that the analytic behavior of Y-functions differs drastically from the case of states with real momenta. Most importantly, Y_Q-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 involve Y_2. Considering yet another example of a three-particle state, we find that the corresponding quantization conditions do not even involve Y_1. Our treatment can be generalized to a wide class of states with complex momenta.
v1, 63 pages, 8 figures
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- Multiple zeta functions and double wrapping in planar N=4 SYM
- Introduction to the thermodynamic Bethe ansatz
- The Quantum Deformed Mirror TBA II
- Hybrid-NLIE for the AdS/CFT spectral problem
- Exceptional Operators in N=4 super Yang-Mills
- Discontinuity relations for the AdS(4)/CFT(3) correspondence
- Contour deformation trick in hybrid NLIE