Analytic Solution of Bremsstrahlung TBA

Abstract

We consider the quark--anti-quark potential on the three sphere or the generalized cusp anomalous dimension in planar N=4 SYM. We concentrate on the vacuum potential in the near BPS limit with $L$ units of R-charge. Equivalently, we study the anomalous dimension of a super-Wilson loop with L local fields inserted at a cusp. The system is described by a recently proposed infinite set of non-linear integral equations of the Thermodynamic Bethe Ansatz (TBA) type. That system of TBA equations is very similar to the one of the spectral problem but simplifies a bit in the near BPS limit. Using techniques based on the Y-system of functional equations we first reduced the infinite system of TBA equations to a Finite set of Nonlinear Integral Equations (FiNLIE). Then we solve the FiNLIE system analytically, obtaining a simple analytic result for the potential! Surprisingly, we find that the system has equivalent descriptions in terms of an effective Baxter equation and in terms of a matrix model. At L=0, our result matches the one obtained before using localization techniques. At all other L's, the result is new. Having a new parameter, L, allows us to take the large L classical limit. We use the matrix model description to solve the classical limit and match the result with a string theory computation. Moreover, we find that the classical string algebraic curve matches the algebraic curve arising from the matrix model.

50 pages, 5 figures. v2: references added, JHEP version

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• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Small deformations of supersymmetric Wilson loops and open spin-chains
• The cusp anomalous dimension at three loops and beyond
• More supersymmetric Wilson loops
• Wilson loops: From four-dimensional SYM to two-dimensional YM
• Complete 1-loop test of AdS/CFT
• Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
• The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
• Wronskian Solution for AdS/CFT Y-system
• Systematics of the cusp anomalous dimension
• Ladders for Wilson Loops Beyond Leading Order
• Exceptional Operators in N=4 super Yang-Mills

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