TY - JOUR

T1 - Analytic solution of Bremsstrahlung TBA

AU - Gromov, Nikolay

AU - Sever, Amit

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - AdS-CFT correspondence

KW - Integrable field theories

KW - Supersymmetric gauge theory

KW - Wilson't hooft and polyakov loops

UR - http://www.scopus.com/inward/record.url?scp=84870424600&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2012)075

DO - 10.1007/JHEP11(2012)075

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AN - SCOPUS:84870424600

SN - 1126-6708

VL - 2012

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 11

M1 - 75

ER -