On Large N Solution of ABJM Theory

We investigate the large N limit of the expectation value W(\lambda) of a BPS Wilson loop in ABJM theory, using an integral expression of the partition function obtained recently by Kapustin et.al. Certain saddle-point equations provide the correct perturbative expansion of W(\lambda). The large \lambda behavior of W(\lambda) is also obtained from the saddle-point equations. The result is compatible with AdS/CFT correspondence.Comment: 27 pages, 4 figures, (v2) references added, the coefficient of order lambda^11 term in Eq.(5.18) corrected, (v3) the estimate of the large lambda behavior corrected, (v4) published version, (v5) comments on revisions added, references adde

AdS/CFT Correspondence as a Consequence of Scale Invariance

We study an anisotropic scale transformation in the worldsheet description of D3-branes in Type IIB theory, and show that the transformation is really a symmetry in a region near D3-branes. AdS/CFT correspondence follows from this symmetry. We will explicitly show that Wilson loops in N=4 supersymmetric Yang-Mills theory and minimal surfaces in AdS_5 are related by the symmetry. The functional form of a supersymmetric Wilson loop operator is naturally derived from our worldsheet point of view.Comment: 20 pages, 8 figures, references adde

Wilson Loops in N=4 Supersymmetric Yang--Mills Theory

Perturbative computations of the expectation value of the Wilson loop in N=4 supersymmetric Yang-Mills theory are reported. For the two special cases of a circular loop and a pair of anti-parallel lines, it is shown that the sum of an infinite class of ladder-like planar diagrams, when extrapolated to strong coupling, produces an expectation value characteristic of the results of the AdS/CFT correspondence, $\sim\exp((constant)\sqrt{g^2N})$. For the case of the circular loop, the sum is obtained analytically for all values of the coupling. In this case, the constant factor in front of $\sqrt{g^2N}$ also agrees with the supergravity results. We speculate that the sum of diagrams without internal vertices is exact and support this conjecture by showing that the leading corrections to the ladder diagrams cancel identically in four dimensions. We also show that, for arbitrary smooth loops, the ultraviolet divergences cancel to order $g^4N^2$.Comment: 24 pages, LaTeX, uses feynmp, 12 postscript figure

More exact predictions of SUSYM for string theory

We compute the coefficients of an infinite family of chiral primary operators in the local operator expansion of a circular Wilson loop in N=4 supersymmetric Yang-Mills theory. The computation sums all planar rainbow Feynman graphs. We argue that radiative corrections from planar graphs with internal vertices cancel in leading orders and we conjecture that they cancel to all orders in perturbation theory. The coefficients are non-trivial functions of the 'tHooft coupling and their strong coupling limits are in exact agreement with those previously computed using the AdS/CFT correspondence. They predict the subleading orders in strong coupling and could in principle be compared with string theory calculations.Comment: 14 pages, 3 figures; v2: misprints correcte

Ladders for Wilson Loops Beyond Leading Order

We set up a general scheme to resum ladder diagrams for the quark-anti-quark potential in N=4 super-Yang-Mills theory, and do explicit calculations at the next-to-leading order. The results perfectly agree with string theory in AdS(5)xS(5) when continued to strong coupling, in spite of a potential order-of-limits problem.Comment: 18 pages, 5 figure

Supersymmetric Open Wilson Lines

In this paper we study Open Wilson Lines (OWL's) in the context of two Supersymmetric Yang Mills theories. First we consider four dimensional N=2 Supersymmetric Yang Mills Theory with hypermultiplets transforming in the fundamental representation of the gauge group, and find supersymmetric OWL's only in the superconformal versions of these theories. We then consider four dimensional N=4 SYM coupled to a three dimensional defect hypermultiplet. Here there is a semi-circular supersymmetric OWL, which is related to the ray by a conformal transformation. We perform a perturbative calculation of the operators in both theories, and discuss using localization to compute them non-perturbatively.Comment: 26 pages, 3 figure

OPE between the energy-momentum tensor and the Wilson loop in N=4 Super-Yang-Mills theory

We analyze the operator product expansion T_{\mu \nu}(z) W[C] in N=4 4-dimensional Super-Yang-Mills (SYM) theory with U(N) gauge group, and clarify that the closed Wilson loop does not possess an anomalous dimension and that only the shape of the loop is changed by the conformal transformation.Comment: 38 pages, 7 figures.(v3) translated into the PTP format (v4) some subtleties correcte

Operators with large R charge in N=4 Yang-Mills theory

It has been recently proposed that string theory in the background of a plane wave corresponds to a certain subsector of the N=4 supersymmetric Yang-Mills theory. This correspondence follows as a limit of the AdS/CFT duality. As a particular case of the AdS/CFT correspondence, it is a priori a strong/weak coupling duality. However, the predictions for the anomalous dimensions which follow from this particular limit are analytic functions of the 't Hooft coupling constant $\lambda$ and have a well defined expansion in the weak coupling regime. This allows one to conjecture that the correspondence between the strings on the plane wave background and the Yang-Mills theory works at the level of perturbative expansions. In our paper we perform perturbative computations in the Yang-Mills theory that confirm this conjecture. We calculate the anomalous dimension of the operator corresponding to the elementary string excitation. We verify at the two loop level that the anomalous dimension has a finite limit when the R charge $J\to \infty$ keeping $\lambda/J^2$ finite. We conjecture that this is true at higher orders of perturbation theory. We show, by summing an infinite subset of Feynman diagrams, under the above assumption, that the anomalous dimensions arising from the Yang-Mills perturbation theory are in agreement with the anomalous dimensions following from the string worldsheet sigma-model.Comment: 26 pages, LaTeX, added references, small changes in the introductio

Wilson Loops in N=2 Super-Yang-Mills from Matrix Model

We compute the expectation value of the circular Wilson loop in N=2 supersymmetric Yang-Mills theory with N_f=2N hypermultiplets. Our results indicate that the string tension in the dual string theory scales as the logarithm of the 't Hooft coupling.Comment: 37 pages, 9 figures; v2: Numerical factors corrected, simple derivation of Wilson loop and discussion of continuation to complex lambda added; v3: instanton partition function re-analyzed in order to take into account a contribution of the hypermultiplet

Exact Results and Holography of Wilson Loops in N=2 Superconformal (Quiver) Gauge Theories

Using localization, matrix model and saddle-point techniques, we determine exact behavior of circular Wilson loop in N=2 superconformal (quiver) gauge theories. Focusing at planar and large `t Hooft couling limits, we compare its asymptotic behavior with well-known exponential growth of Wilson loop in N=4 super Yang-Mills theory. For theory with gauge group SU(N) coupled to 2N fundamental hypermultiplets, we find that Wilson loop exhibits non-exponential growth -- at most, it can grow a power of `t Hooft coupling. For theory with gauge group SU(N) x SU(N) and bifundamental hypermultiplets, there are two Wilson loops associated with two gauge groups. We find Wilson loop in untwisted sector grows exponentially large as in N=4 super Yang-Mills theory. We then find Wilson loop in twisted sector exhibits non-analytic behavior with respect to difference of two `t Hooft coupling constants. By letting one gauge coupling constant hierarchically larger/smaller than the other, we show that Wilson loops in the second type theory interpolate to Wilson loop in the first type theory. We infer implications of these findings from holographic dual description in terms of minimal surface of dual string worldsheet. We suggest intuitive interpretation that in both type theories holographic dual background must involve string scale geometry even at planar and large `t Hooft coupling limit and that new results found in the gauge theory side are attributable to worldsheet instantons and infinite resummation therein. Our interpretation also indicate that holographic dual of these gauge theories is provided by certain non-critical string theories.Comment: 52 pages, 7 figures v2. more figures embedded v3. minor stylistic changes, v4. published versio