Near BPS Wilson loop in β-deformed theories

Abstract

We propose a definition of the Wilson loop operator in the N = 1 β-deformed supersymmetric Yang-Mills theory. Although the operator is not BPS, it has a finite expectation value at least up to order (g 2 N) 2 . This does not happen generally for a generic non-BPS Wilson loop whose expectation value is UV divergent. For this reason we call this a near-BPS Wilson loop and conjecture that its exact expectation value is finite. We derive the general form of the boundary condition satisfied by the dual string worldsheet and find that it is deformed. Finiteness of the expectation value of the Wilson loop, together with some rather remarkable properties of the Lunin-Maldacena metric and the B-field, fixes the boundary condition to be one which is characterized by the vielbein of the deformed supergravity metric. The Wilson loop operators provide natural candidates as dual descriptions to some of the existing D-brane configurations in the Lunin-Maldacena background. We also construct the string dual configuration for a near-1/4 BPS circular Wilson loop operator. The string lies on a deformed three-sphere instead of a two-sphere as in the undeformed case. The expectation value of the Wilson loop operator is computed using the AdS/CFT correspondence and is found to be independent of the deformation. We conjecture that the exact expectation value of the Wilson loop is given by the same matrix model as in the undeformed case.

On marginal deformations and non-integrability

“…In fact, the real β-deformed theory has been studied extensively (see [18] for a review in the context of AdS/CFT integrability) and, in several cases, has been found to resemble closely, although non-trivially, the results of its undeformed parent theory. For example, the expectation values of particular BPS-like Wilson loops [19] remain undeformed. Moreover, a Lax pair for the real β-deformation was explicitly constructed in [20] by relating the deformed system to the undeformed one, therefore establishing integrability.…”

Generalised cusp anomalous dimension in β−deformed super Yang Mills theory

“…Our choice can be justified from several points of view. It has been found that the 1/4 BPS-like Wilson loop in the β deformed theory in the strong coupling limit has undeformed expectation value [13]. This has also been proved in the case of higher representation Wilson loops in [14].…”

“…In this paper we have calculated the cusp anomalous dimension of the Wilson loop in β deformed gauge/gravity duality. An interesting feature of this theory is that several BPS-like quantities, have an undeformed expectation value in the strong coupling limit, for example as [13,14]. This fact enables us to make a conjecture for the from of the cusp anomalous dimensions for every λ.…”

Gluon scattering in deformed N=4 SYM

“…In this note we will consider gluon and gluino scattering amplitudes and the corresponding light-like Wilson loops in large N β-deformed N = 4 SYM with real β (for a discussion of Wilson loops in the β-deformed theory see [12]). This deformation breaks the N = 4 supersymmetry to N = 1.…”