No abstract

We discuss the impact of quadratic quantum fluctuations on the Wilson loop extracted from classical string theory. We show that a large class of models, which includes the near horizon limit of D p branes with 16 supersymmetries, admits a Lüscher type correction to the classical potential. We confirm that the quantum determinant associated with a BPS configuration of a single quark in the AdS 5 ×S 5 model is free from divergences. We find that for the Wilson loop in that model, unlike the situation in flat space-time, the fermionic determinant does not cancel the bosonic one. For string models that correspond to gauge theories in the confining phase, we show that the correction to the potential is of a Lüscher type and is attractive.

We study a deformation of the type IIB Maldacena-Nuñez background which arises as the near-horizon limit of NS5 branes wrapped on a two-cycle. This background is dual to a "little string theory" compactified on a two-sphere, a theory which at low energies includes four-dimensional N = 1 super Yang-Mills theory. The deformation we study corresponds to a mass term for some of the scalar fields in this theory, and it breaks supersymmetry completely. In the language of seven-dimensional SO(4) gauged supergravity the deformation involves (at leading order) giving a VEV, depending only on the radial coordinate, to a particular scalar field. We explicitly construct the corresponding solution at leading order in the deformation, both in seven-dimensional and in ten-dimensional supergravity, and we verify that it completely breaks supersymmetry. Since the original background had a mass gap and we are performing a small deformation, the deformed background is guaranteed to be stable even though it is not supersymmetric.1 E-mail : Ofer.Aharony@weizmann.ac.il. Incumbent of the Joseph and Celia Reskin career development chair.2

ABSTRACT. We give two algorithms that allow to get arbitrary precision asymptotics for the harmonic potential of a random walk.

We compute the M theory corrections to the confining linear potential between a quark and an anti-quark in N = 1 Super Yang-Mills theory. We find a constant term, and a term exponentially small with characteristic length of Λ −1 QCD . The potential in the MQCD setup that corresponds to softly broken N = 1 SYM is found to have a similar behavior.