Holography and the Higgs branch of N=2 SYM theories

We present a proposal for the description of the Higgs branch of four-dimensional N=2 supersymmetric Yang-Mills theories in the context of the AdS/CFT correspondence. We focus on a finite Sp(N) N=2 theory arising as dual of a configuration of N D3-branes in the vicinity of four D7-branes and an orientifold 7-plane in type I' string theory. The field theory contains hypermultiplets in the second rank anti-symmetric and in the fundamental representations. The Higgs branch has a dual description in terms of gauge field configurations with non-zero instanton number on the world-volume of the D7-branes. In this setting the non-renormalisation of the metric on the Higgs branch implies constraints on the alpha' corrections to the D7-brane effective action, including couplings to the curvature and five-form field strength. In the second part of the paper we discuss non-renormalisation properties of BPS Wilson lines, which are closely related to the physics of the Higgs branch. Using a formulation of the four-dimensional N=2 theory in terms of a three-dimensional N=2 superspace we show that the expectation value of certain Wilson-line operators with hypermultiplets at the end points is independent of the length and thus coincides with the expectation value of the local operators parametrising the Higgs branch.Comment: LaTeX, 29 pages, 1 figure; v2: minor corrections, one reference adde

Membranes from monopole operators in ABJM theory: large angular momentum and M-theoretic AdS_4/CFT_3

We consider states with large angular momentum to facilitate the study of the M-theory regime of the AdS_4/CFT_3 correspondence. We study the duality between M-theory in AdS_4xS^7/Z_k and the ABJM N=6 Chern-Simons-matter theory with gauge group U(N)xU(N) and level k, taking N large and k of order 1. In this regime the lack of an explicit formulation of M-theory in AdS_4xS^7/Z_k makes the gravity side difficult, while the CFT is strongly coupled and the planar approximation is not applicable. To overcome these difficulties, we focus on states on the gravity side with large angular momentum J>>1 and identify the dual operators in the CFT, thereby establishing the AdS/CFT dictionary in this sector. Natural approximation schemes arise on both sides thanks to the presence of the small parameter 1/J. On the AdS side, we use the matrix model of M-theory on the maximally supersymmetric pp-wave background with matrices of size J/k. A perturbative treatment of this matrix model provides a good approximation to M-theory in AdS_4xS^7/Z_k when N^{1/3}<<J<<N^{1/2}. On the CFT side, we study the theory on S^2xR with magnetic flux J/k. A Born-Oppenheimer type expansion arises naturally for large J in spite of the theory being strongly coupled. The energy spectra on the two sides agree at leading order. This provides a non-trivial test of the AdS_4/CFT_3 correspondence including near-BPS observables associated with membrane degrees of freedom, thus verifying the duality beyond the previously studied sectors corresponding to either BPS observables or the type IIA string regime.Comment: 67 pages, 5 figures; V2: minor changes, references adde

N=4 supersymmetric Yang-Mills theory and the AdS/SCFT correspondence

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 chapters 3, 4 and 5. A systematic re-analysis of the perturbative properties of the theory is presented in the third chapter. Two-, three- and four-point Green functions of elementary fields are computed using the component formulation and/or the superfield approach and subtleties related to the gauge-fixing are pointed out. In the fourth chapter, after an introduction to instanton calculus in supersymmetric gauge theories, the computation of the one-instanton contributions to Green functions of gauge invariant composite operators in the semiclassical approximation is reported. The calculations of four-, eight- and sixteen-point Green functions of operators in the supercurrent multiplet are reviewed in detail. The final chapter is devoted to the AdS/SCFT correspondence. Some general aspects are discussed. Then the attention is focused on the relation between instantons in N=4 SYM and D-instanton effects in type IIB string theory. The comparison between instanton contributions to Green functions of composite operators in the boundary field theory and D-instanton generated terms in the amplitudes computed in type IIB string theory is performed and agreement between these two sources of non-perturbative effects is shown.Comment: 228 pages, Ph.D. thesis, LaTeX2e, uses the feynmp, fencyhdr, graphicx and AMS package

Properties of the Konishi multiplet in N=4 SYM theory

We study perturbative and non-perturbative properties of the Konishi multiplet in N=4 SYM theory in D=4 dimensions. We compute two-, three- and four-point Green functions with single and multiple insertions of the lowest component of the multiplet, and of the lowest component of the supercurrent multiplet. These computations require a proper definition of the renormalized operator and lead to an independent derivation of its anomalous dimension. The O(g^2) value found in this way is in agreement with previous results. We also find that instanton contributions to the above correlators vanish. From our results we are able to identify some of the lowest dimensional gauge-invariant composite operators contributing to the OPE of the correlation functions we have computed. We thus confirm the existence of an operator belonging to the representation 20', which has vanishing anomalous dimension at order g^2 and g^4 in perturbation theory as well as at the non-perturbative level, despite the fact that it does not obey any of the known shortening conditions.Comment: 23 pages, latex, no figure

On the logarithmic behaviour in N=4 SYM theory

We show that the logarithmic behaviour seen in perturbative and non perturbative contributions to Green functions of gauge-invariant composite operators in N=4 SYM with SU(N) gauge group can be consistently interpreted in terms of anomalous dimensions of unprotected operators in long multiplets of the superconformal group SU(2,2|4). In order to illustrate the point we analyse the short-distance behaviour of a particularly simple four-point Green function of the lowest scalar components of the N=4 supercurrent multiplet. Assuming the validity of the Operator Product Expansion, we are able to reproduce the known value of the one-loop anomalous dimension of the single-trace operators in the Konishi supermultiplet. We also show that it does not receive any non-perturbative contribution from the one-instanton sector. We briefly comment on double- and multi-trace operators and on the bearing of our results on the AdS/SCFT correspondence.Comment: 18 pages, Late

Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory

The one-instanton contributions to various correlation functions of supercurrents in four-dimensional N=4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory.Expressions of the same form are obtained from the leading effects of a single D-instanton extracted from the IIB superstring effective action around the AdS5*S5 background. This is in line with the suggested AdS/Yang-Mills correspondence. The relation between Yang--Mills instantons and D-instantons is further confirmed by the explicit form of the classical D-instanton solution in the AdS5*S5 background and its associated supermultiplet of zero modes. Speculations are made concerning instanton effects in the large-N_c limit of the SU(N_c) Yang-Mills theory.Comment: 41 pages, LaTeX. Typos corrected and minor clarifications adde

Less is More: Non-renormalization Theorems from Lower Dimensional Superspace

We discuss a new class of non-renormalization theorems in N=4 and N=2 Super-Yang-Mills theory, obtained by using a superspace which makes a lower dimensional subgroup of the full supersymmetry manifest. Certain Wilson loops (and Wilson lines) belong to the chiral ring of the lower dimensional supersymmetry algebra, and their expectation values can be computed exactly.Comment: 8 pages, based on talk given by Z. Guralnik at 8th Workshop on Non-perturbative QCD, Paris, June 200

Towards a tensionless string field theory for the N=(2,0) CFT in d=6

We describe progress in using the field theory of tensionless strings to arrive at a Lagrangian for the six-dimensional N=(2,0) conformal theory. We construct the free part of the theory and propose an ansatz for the cubic vertex in light-cone superspace. By requiring closure of the (2,0) supersymmetry algebra, we fix the cubic vertex up to two parameters