We present evidence that loop amplitudes in maximally supersymmetric (N=4) Yang-Mills theory (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full N=4 SYM has only logarithmic singularities and is free of any poles at infinity--properties closely related to uniform transcende...

We explicitly compute the complete three-loop (O(g 4)) contribution to the four-point function of chiral primary current-like operators˜q 2 q 2 ˜ q 2 q 2 in any finite N = 2 SYM theory. The computation uses N = 2 harmonic supergraphs in coordinate space. Dramatic simplifications are achieved by a double insertion of the N = 2 SYM linearized action, and application of supercon-formal covariance ...

Abstract We prove that the half-BPS Wilson loop operator of N = 4 SYM in a symmetric representation of the gauge group has a bulk gravitational description in terms of a single D3-brane in AdS5×S, as argued in hep-th/0604007. We also show that a half-BPS Wilson loop operator in an arbitrary representation is described by the D3-brane configuration proposed in hep-th/0604007. This is demonstrate...

This paper introduces a software tool SYM-LS-SVM-SOLVER written in Maple to derive the dual system and the dual model representation of LS-SVM based models, symbolically. SYM-LS-SVM-SOLVER constructs the Lagrangian from the given objective function and list of constraints. Afterwards it obtains the KKT (Karush-Kuhn-Tucker) optimality conditions and finally formulates a linear system in terms of...

We develop a novel bi-harmonic $\mathcal{N}=4$ superspace formulation of the supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, SYM superfield constraints are solved terms on-shell $\mathcal {N}=2$ harmonic superfields. Such an approach provides convenient tool constructing manifestly invariants and further rewriting them $\mathcal{N}= 2$ superspace. particular, we pre...

The properties of gauge-invariant composite operators and their correlation functions in N = 4 SYM are discussed in the analytic superspace formalism. A complete classification of the different types of operators in the theory is given. Operators can be either protected or unprotected according to whether they do not or do have anomalous dimensions, and the analytic superspace formalism allows ...

Q: H ow long have y o u been dean o f students, a n d w ha t is the role o f the dean a t Sa in t M ary’s? A: My title really isn't clean of stu ­ dents, it's dean of student affairs. I cam e to Saint Mary’s in August of 1976, so this is my fifth year. Dean of Student Affairs is a senior office posi­ tion so that I report directly to the president. There are eight different departm ents and eac...

We formulate and prove a topological Paley-Wiener theorem for the normalized spherical Laplace transform deened on the rank 1 causal sym