Abstract

ABSTRACT: We consider the quark anti-quark potential on the three sphere in planar N = 4 SYM and the associated vacuum potential in the near BPS limit with L units of R-charge. The associated Bremsstrahlung function B L has been recently computed ana-lytically by means of the Thermodynamical Bethe Ansatz. We discuss it at strong coupling by computing it at large but finite L. We provide strong support to a special symmetry of the Bremsstrahlung function under the formal discrete Z 2 symmetry L! 1 L. In this context, it is the counterpart of the reciprocity invariance discovered in the past in the spectrum of various gauge invariant composite operators. The Z 2 symmetry has remark-able consequences in the scaling limit where L is taken to be large with fixed ratio to the ’t Hooft coupling. This limit organizes in inverse powers of the coupling and resembles the semiclassical expansion of the dual string theory which is indeed known to capture the leading classical term. We show that the various higher-order contributions to the Bremsstrahlung function obey several constraints and, in particular, the next-to-leading term, formally associated with the string one-loop correction, is completely determined by the classical contribution. The large L limit at strong coupling is also discussed.ar X iv