Deconstructing Supersymmetric S-matrices in D <= 2 + 1

Global supersymmetries of the S-matrices of N = 2, 4, 8 supersymmetric Yang-Mills theories in three spacetime dimensions (without matter hypermultiplets) are shown to be SU(1|1), SU(2|2) and SU(2|2) X SU(2|2) respectively. These symmetries are not manifest in the off-shell Lagrangian formulations of these theories. A direct map between these symmetries and their representations in terms of the Yang-Mills degrees of freedom and the corresponding quantities in Chern-Simons-Matter theories with N >= 4 supersymmetry is also obtained. Dimensional reduction of the on-shell observables of the Yang-Mills theories to two spacetime dimensions is also discussed.Comment: 1+13 page

Wilson Loops in N=2 Superconformal Yang-Mills Theory

We present a three-loop O(g^6) calculation of the difference between the expectation values of Wilson loops evaluated in N=4 and superconformal N=2 supersymmetric Yang-Mills theory with gauge group SU(N) using dimensional reduction. We find a massive reduction of required Feynman diagrams, leaving only certain two-matter-loop corrections to the gauge field and associated scalar propagator. This "diagrammatic difference" leaves a finite result proportional to the bare propagators and allows the recovery of the zeta(3) term coming from the matrix model for the 1/2 BPS circular Wilson loop in the N=2 theory. The result is valid also for closed Wilson loops of general shape. Comments are made concerning light-like polygons and supersymmetric loops in the plane and on S^2.Comment: 16 pages. v2 minor changes, to appear in JHEP. v3 corrected reference

Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals

We study Wilson loops in the three-dimensional N=6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena, that is conjectured to be dual to type IIA string theory on AdS_4 x CP^3. We construct loop operators in the Chern-Simons theory which preserve 1/6 of the supercharges and calculate their expectation value up to 2-loop order at weak coupling. The expectation value at strong coupling is found by constructing the string theory duals of these operators. For low dimensional representations these are fundamental strings, for high dimensional representations these are D2-branes and D6-branes. In support of this identification we demonstrate that these string theory solutions match the symmetries, charges and the preserved supersymmetries of their Chern-Simons theory counterparts.Comment: 28 pages. v2: references added, choice of the Wilson loop operator clarified; v3: combinatorial factor of 2 in perturbative calculation corrected; v4: typos corrected, version to be publishe

On the Regularization of Extremal Three-point Functions Involving Giant Gravitons

In the AdS_5/CFT_4 set-up, extremal three-point functions involving two giant 1/2 BPS gravitons and one point-like 1/2 BPS graviton, when calculated using semi-classical string theory methods, match the corresponding three-point functions obtained in the tree-level gauge theory. The string theory computation relies on a certain regularization procedure whose justification is based on the match between gauge and string theory. We revisit the regularization procedure and reformulate it in a way which allows a generalization to the ABJM set-up where three-point functions of 1/2 BPS operators are not protected and where a match between tree-level gauge theory and semi-classical string theory is hence not expected.Comment: 5 pages, no figures. v2 updated reference

Counting Bubbles in Linear Chord Diagrams

In a linear chord diagram a short chord is one which joins adjacent vertices. We define a bubble to be a region in a linear chord diagram devoid of short chords. We derive a formal generating function counting bubbles by their size and find an exact result for the mean bubble size. We find that once one discards diagrams which have no short chords at all, the distribution of bubble sizes is given by a smooth function in the limit of long diagrams. Using a summation over short chords, the exact form of this asymptotic distribution is found.Comment: 9 pages, 3 figure

Free Energy and Phase Transition of the Matrix Model on a Plane-Wave

It has recently been observed that the weakly coupled plane wave matrix model has a density of states which grows exponentially at high energy. This implies that the model has a phase transition. The transition appears to be of first order. However, its exact nature is sensitive to interactions. In this paper, we analyze the effect of interactions by computing the relevant parts of the effective potential for the Polyakov loop operator in the finite temperature plane-wave matrix model to three loop order. We show that the phase transition is indeed of first order. We also compute the correction to the Hagedorn temperature to order two loops.Comment: 24 page

To Dream The Old Dreams For Me

https://digitalcommons.library.umaine.edu/mmb-vp/6509/thumbnail.jp