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 show that the matrix formulation of non-commutative field theories is equivalent, in the continuum, to a formulation in a mixed configuration-momentum space. In this formulation, the non-locality of the interactions, that leads to the IR/UV mixing, becomes transparent. We clarify the relation between long range effects (and IR divergences) and the non-planarity of the corresponding Feynman diagrams.

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.

We look at the string theory dual of the N = 1 * theory, involving 5-branes, which was recently proposed by Polchinski and Strassler [1]. We argue that SUGRA alone is not enough in order to obtain the correct screening and confinement behaviour of the various massive field theory vacua, but that appropriate worldvolume phenomena of the 5-branes must be included. We therefore work within the SUGRA approximation, also taking into account the brane dynamics, and classify all the SUGRA configurations. In this level of analysis, we find multiple valid configurations for every given vacuum. We discuss some possible resolutions of this perplexing result. We also consider the spectrum of asymptotic states, and discuss the global symmetries of the SUGRA solution of the N = 1 * theory and of the N = 0 * theory obtained from it by explicit supersymmetry breaking.