Bremsstrahlung function, leading Lüscher correction at weak coupling and localization

Marisa Bonini,Domenico Seminara,Luca Griguolo,Michelangelo Preti

doi:10.1007/jhep02(2016)172

Marisa Bonini, Domenico Seminara + Show 2 more

Open Access

https://doi.org/10.1007/jhep02(2016)172

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Abstract

We discuss the near BPS expansion of the generalized cusp anomalous dimension with L units of R-charge. Integrability provides an exact solution, obtained by solving a general TBA equation in the appropriate limit: we propose here an alternative method based on supersymmetric localization. The basic idea is to relate the computation to the vacuum expectation value of certain 1/8 BPS Wilson loops with local operator insertions along the contour. These observables localize on a two-dimensional gauge theory on S^2, opening the possibility of exact calculations. As a test of our proposal, we reproduce the leading Luscher correction at weak coupling to the generalized cusp anomalous dimension. This result is also checked against a genuine Feynman diagram approach in N=4 Super Yang-Mills theory.

Highlights

Angle θ that controls the coupling of the scalars to the two halves of the cusp [23]
The basic idea is to relate the computation to the vacuum expectation value of certain 1/8 BPS Wilson loops with local operator insertions along the contour
For general correlation functions of certain 1/8 BPS Wilson loops and local operators inserted on a S2 in space-time, localization reduces N = 4 SYM to a 2d Hitchin/Higgs-Yang-Mills theory, that turns out to be equivalent to the two-dimensional pure Yang-Mills theory (YM2) on S2 in its zero-instanton sector

Summary

DM Tr eiM exp

The expansion (2.4) was obtained in [25] by considering a small deformation of the so-called wedge It is a loop in the class (2.1) which consists of two meridians separated by an angle π − φ. We choose to insert two of these operators: one in the north pole [xμN = (0, 0, 1)] and the other in the south pole [xμS = (0, 0, −1)] In these special positions they reduce to the holomorphic and the anti-holomorphic combination of two of the scalar fields which do not couple to the loop. Applying the same argument given in [25], one can argue (since the relevant deformation never involves the poles) that

The wedge on S2 with field strength insertions in YM2

Perturbative computation of the Luscher term from YM2 on the sphere

General setting for perturbative computations on S2

Operator insertions of length L

Conclusions and outlook