Stefano Kovacs

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

The one-instanton contributions to various correlation functions of superconformal currents in four-dimensional = 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-Nc limit of the SU(Nc) Yang-Mills theory.

Proof of all-order finiteness for planar beta-deformed Yang-Mills

We study a marginal deformation of N = 4 Yang–Mills, with a real deformation parameter β. This β-deformed model has only N = 1 supersymmetry and a U(1)×U(1) flavor symmetry. The introduction of a new superspace ⋆-product allows us to formulate the theory in N = 4 light-cone superspace, despite the fact that it has only N = 1 supersymmetry. We show that this deformed theory is conformally invariant, in the planar approximation, by proving that its Green functions are ultra-violet finite to all orders in perturbation theory.

Non-renormalisation of extremal correlators in N=4 SYM theory

We show that extremal correlators of chiral primary operators in N=4 supersymmetric Yang–Mills theory with SU(N) gauge group are neither renormalised at first (g2) order in perturbation theory nor receive contribution from any instanton sector at leading order in the semiclassical expansion. This lends support to the strongest version of a new prediction recently put forward on the basis of the AdS/SCFT correspondence.

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 = 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 = 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.

On instanton contributions to anomalous dimensions in N =4 supersymmetric Yang-Mills theory

Instanton contributions to the anomalous dimensions of gauge-invariant composite operators in the N =4 supersymmetric SU(N) Yang–Mills theory are studied in the one-instanton sector. Independent sets of scalar operators of bare dimension �0 ≤ 5 are constructed in all the allowed representations of the SU(4) R-symmetry group and their two-point functions are computed in the semiclassical approximation. Analysing the moduli space integrals the sectors in which the scaling dimensions receive non-perturbative contributions are identified. The requirement that the integrations over the fermionic collective coordinates which arise in the instanton background are saturated leads to non-renormalisation properties for a large class of operators. Instanton-induced corrections to the scaling dimensions are found only for dimension 4 SU(4) singlets and for dimension 5 operators in the 6 of SU(4). In many cases the non-renormalisation results are argued to be specific to operators of small dimension, but for some special sectors it is shown that they are valid for arbitrary dimension. Comments are also made on the implications of the results on the form of the instanton contributions to the dilation operator of the theory and on the possibility of realising its action on the instanton moduli space.

On the logarithmic behaviour in Script 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 = 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 = 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.

Non-perturbative contributions to the plane-wave string mass matrix

D-instanton contributions to the mass matrix of arbitrary excited string states of type IIB string theory in the maximally supersymmetric plane-wave background are cal- culated to leading order in the string coupling using a supersymmetric light-cone boundary state formalism. The explicit non-perturbative dependence of the mass matrix on the com- plex string coupling, the plane-wave mass parameter and the mode numbers of the excited states is determined.

AdS/CFT Duality and the Higgs Branch of N = 2 SYM

We construct the AdS description of the Higgs branch of the finite = 2 Sp(N) gauge theory with one antisymmetric hypermultiplet and four fundamental hypermultiplets. Holography, combined with the non-renormalization of the metric on the Higgs branch, leads to novel constraints on unknown terms in the non-abelian Dirac-Born-Infeld action. These terms include non-minimal couplings of D-branes to bulk supergravity fields.

Mixing of the RR and NSNS sectors in the Berenstein-Maldacena-Nastase limit

This paper concerns instanton contributions to two-point correlation functions of BMN operators in N =4 supersymmetric Yang–Mills that vanish in planar perturbation theory. Two-point functions of operators with even numbers of fermionic impurities (dual to R⊗R string states) and with purely scalar impurities (dual to NS⊗NS string states) are considered. This includes mixed R⊗R–NS⊗NS two-point functions. The gauge theory correlation functions are shown to respect BMN scaling and their behaviour is found to be in good agreement with the corresponding D-instanton contributions to two-point amplitudes in the maximally supersymmetric IIB plane-wave string theory. The string theory calculation also shows a simple dependence of the mass matrix elements on the mode numbers of states with an arbitrary number of impurities, which is difficult to extract from the gauge theory. For completeness, a discussion is also given of the perturbative mixing of two-impurity states in the R⊗R and NS⊗NS sectors at the first non-planar level.

A PERTURBATIVE REANALYSIS OF

The finiteness properties of the supersymmetric Yang–Mills theory are reanalyzed both in the component formulation and using superfields, in order to discuss some subtleties that emerge in the computation of gauge dependent quantities. The one-loop corrections to various Green functions of elementary fields are calculated. In the component formulation it is shown that the choice of the Wess–Zumino gauge, that is standard in supersymmetric gauge theories, introduces ultraviolet divergences in the propagators at the one-loop level. Such divergences are exactly canceled when the contributions of the fields that are put to zero in the Wess–Zumino gauge are taken into account. In the description in terms of superfields, infrared divergences are found for every choice of gauge different from the supersymmetric generalization of the Fermi–Feynman gauge. Two-, three- and four-point functions of superfields are computed and some general features of the infrared problem are discussed. We also examine the effect of the introduction of mass terms for the (anti)chiral superfields in the theory, which break supersymmetry from to . It is shown that in the mass deformed model no ultraviolet divergences appear in two-point functions. It is argued that this result can be generalized to n-point functions, supporting the proposal of a possible of use of this modified model as a supersymmetry-preserving regularization scheme for theories.