Wilson loops from supergravity and string theory

We present a theorem that determines the value of the Wilson loop associated with a Nambu-Goto action which generalizes the action of the $AdS_5\times S_5$ model. In particular we derive sufficient conditions for confining behavior. We then apply this theorem to various string models. We go beyond the classical string picture by incorporating quadratic quantum fluctuations. We show that the bosonic determinant of $D_p$ branes with 16 supersymmetries yields a Luscher term. We confirm that the free energy associated with a BPS configuration of a single quark is free from divergences. We show that unlike for a string in flat space time in the case of $AdS_5\times S_5$ the fermionic determinant does not cancel the bosonic one. For a setup that corresponds to a confining gauge theory the correction to the potential is attractive. We determine the form of the Wilson loop for actions that include non trivial $B_{\mu\nu}$ field. The issue of an exact determination of the value of the stringy Wilson loop is discussed. Talk presented in string 99 Potsdam.Comment: 12 pages Late

A note on the integral equation for the Wilson loop in N = 2 D=4 superconformal Yang-Mills theory

We propose an alternative method to study the saddle point equation in the strong coupling limit for the Wilson loop in $\mathcal{N}=2$ D=4 super Yang-Mills with an SU(N) gauge group and 2N hypermultiplets. This method is based on an approximation of the integral equation kernel which allows to solve the simplified problem exactly. To determine the accuracy of this approximation, we compare our results to those obtained recently by Passerini and Zarembo. Although less precise, this simpler approach provides an explicit expression for the density of eigenvalues that is used to derive the planar free energy.Comment: 12 pages, v2: section 2.5 (Free Energy) amended and reference added, to appear in J. Phys.

Wilson Loops in Large N Theories

Talk presented at Strings '99 in Potsdam, Germany (July 19 - 24, 1999).Comment: 11 pages; submitted to Proceedings of Strings '9

Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings

We evaluate the exact one-loop partition function for fundamental strings whose world-surface ends on a cusp at the boundary of AdS_4 and has a "jump" in CP^3. This allows us to extract the stringy prediction for the ABJM generalized cusp anomalous dimension Gamma_{cusp}^{ABJM} (phi,theta) up to NLO in sigma-model perturbation theory. With a similar analysis, we present the exact partition functions for folded closed string solutions moving in the AdS_3 parts of AdS_4 x CP^3 and AdS_3 x S^3 x S^3 x S^1 backgrounds. Results are obtained applying to the string solutions relevant for the AdS_4/CFT_3 and AdS_3/CFT_2 correspondence the tools previously developed for their AdS_5 x S^5 counterparts.Comment: 48 pages, 2 figures, version 3, corrected misprints in formulas 2.12, B.86, C.33, added comment on verification of the light-like limi

D-Instantons and asymptotic geometries

The large N limit of D3-branes is expected to correspond to a superconformal field theory living on the boundary of the anti-de Sitter space appearing in the near-horizon geometry. Dualizing the D3-brane to a D-instanton, we show that this limit is equivalent to a type IIB S-duality. In both cases one effectively reaches the near-horizon geometry. This provides an alternative approach to an earlier derivation of the same result that makes use of the properties of a gravitational wave instead of the D-instanton.Comment: 17 pages, LaTeX, 1 figure, minor corrections and refs adde

A Note on D-Branes of Odd Codimensions from Noncommutative Tachyons

On a noncommutative space of rank-1, we construct a codimension-one soliton explicitly and, in the context of noncommutative bosonic open string theory, identify it with the D24-brane. We compute the tension of the proposed D24-brane, yielding an exact value and show that it is related to the tension of the codimension two D23-brane by the string T-duality. This resolves a puzzle posed by the result of Harvey, Kraus, Larsen and Martinec. We also apply the result to non-BPS branes in superstring theories and argue that the codimension-one soliton gives rise to new descent relation among the non-BPS branes in Type IIA and Type IIB string theories via T-duality