Green Functions of N=1 SYM and Radial/Energy-Scale Relation

We solve N=(8,8) super Yang-Mills theory in 1+1 dimensions at strong coupling to directly confirm the predictions of supergravity at weak coupling. We do our calculations in the large-N_c approximation using Supersymmetric Discrete Light-Cone Quantization with up to 3*10^{12} basis states. We calculate the stress-energy correlator <T^{++}(r) T^{++}(0)> as a function of the separation r and find that at intermediate values of r the correlator behaves as r^{-5} to within errors...

Much of modern string theory research concerns AdS/CFT duality, or more generally, gauge/gravity duality. The main subjects are a) Testing and understanding such dualities by exploring how they work for systems with a lot of supersymmetry b) Constructing and exploring approximate string theory duals of QCD c) Applying gauge/gravity duality to other areas of physics such as condensed matter and nuclear physics. I will briefly discuss the first topic.

Recently the exact NSVZ $\beta$-function was rewritten in the form of a relation between the $\beta$-function and the anomalous dimensions of the quantum gauge superfield, of the Faddeev--Popov ghosts, and of the matter superfields. It was also suggested that this form of the NSVZ equation follows from an underlying equation relating two-point Green functions of the theory. Here we demonstrate that this relation is satisfied at the two-loop level for the non-Abelian ${\cal N}...

We prove that the AdS/CFT calculation of 1-point functions can be drastically simplified by using variational arguments. We give a simple universal proof, valid for any theory that can be derived from a Lagrangian, that the large radius divergencies in 1-point functions can always be renormalized away (at least in the semiclassical approximation). The renormalized 1-point functions then follow by a simple variational problem involving only finite quantities. Several examples,...

This dissertation reviews various aspects of the N=4 supersymmetric Yang--Mills theory in particular in relation with the AdS/CFT correspondence. The first two chapters are introductory. The first one contains a description of the general properties of rigid supersymmetric theories in four dimensions both at the classical and at the quantum level. The second chapter is a review of the main properties of the N=4 SYM theory under consideration. Original results are reported in ...

We report on progress in evaluating quantum filed theories with supersymmetric discrete light-cone quantization (SDLCQ). We compare the method to lattice gauge theory and point out its relevance for lattice calculations. As an exciting application we present a test of the Maldacena conjecture. We test the conjecture by evaluating the correlator of the stress-energy tensor in the strong coupling field theory and comparing to the string theory prediction of its behavior as a fu...

We consider non-perturbative effects in the beta-deformed N=4 supersymmetric gauge theory in the context of the AdS/CFT correspondence. We concentrate on the correlators of the Yang-Mills operators which correspond to the lowest Kaluza-Klein modes propagating on the dual supergravity background found by Lunin and Maldacena in hep-th/0502086. In particular, we calculate all multi-instanton contributions to these correlators in the beta-deformed SYM and find a compelling agreem...

We consider the operators with highest anomalous dimension $\Delta$ in the compact rank-one sectors $\mathfrak{su}(1|1)$ and $\mathfrak{su}(2)$ of ${\cal N}=4$ super Yang-Mills. We study the flow of $\Delta$ from weak to strong 't Hooft coupling $\lambda$ by solving (i) the all-loop gauge Bethe Ansatz, (ii) the quantum string Bethe Ansatz. The two calculations are carefully compared in the strong coupling limit and exhibit different exponents $\nu$ in the leading order expans...

It has recently been conjectured that the AdS_5/SYM_4 correspondence can be generalized away from the conformal limit, to a duality between supergravity on the full asymptotically flat three-brane background and a theory characterized as N=4 SYM deformed in the IR by a specific dimension-eight operator. Assuming that this relation is valid, we derive a prescription for computing n-point correlation functions in the holographic theory, which reduces to the standard AdS/CFT rec...

We provide a characterization of the set of configurations in N=4 SYM theory that are dual to small AdS black holes. Our construction shows that the black hole dual states are approximately thermal on a SU(M) subset of degrees of freedom of a SU(N) gauge theory. M is determined dynamically and the black hole degrees of freedom are dynamically insulated from the rest. These states are localized on the S^5 and have dynamical processes that correspond to matter absorption that m...