arXiv subjects

Stefano Kovacs

Publications and source records attributed to Stefano Kovacs.

25 records · Page 2Linked to original sources

arXiv2001

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.

hep-th↗

arXiv1999

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 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.

hep-th↗

arXiv1999

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.

hep-th↗

arXiv1999

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.

hep-th↗

arXiv1999

A perturbative re-analysis of N=4 supersymmetric Yang--Mills theory

The finiteness properties of the N=4 supersymmetric Yang-Mills theory are reanalyzed both in the component formulation and using N=1 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 cancelled 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 N=1 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 N=1 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 N=4 to N=1. It is shown that in the mass deformed model no ultraviolet divergences appear in two-point functions. It 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 N=1 theories.

hep-th↗

arXiv1998

Yang-Mills instantons vs. type IIB D-instantons

We report on the computation of the one-instanton contribution to the 16-point Green function of fermionic composite operators in N=4 Super YM theory. The remarkable agreement, initially found in the case of an SU(2) gauge group, with the one D-instanton contribution to the corresponding type IIB superstring amplitude on $AdS_5\times S^5$ is reviewed here. The recent extension by other authors of this result to any SU(N) gauge group and to multi-instantons in the large N limit is briefly discussed. We also argue that for the AdS/SCFT correspondence under consideration to work for any $N\geq 2$, at least for some protected interactions, string effects should require a truncation of the Kaluza--Klein spectrum for finite $S^5$ radius much in the same way as worldsheet unitarity restricts the allowed isospins in SU(2) WZW models. Finally, we briefly comment on the logarithmic behavior of some four-point Green functions of scalar composite operators.

hep-th↗

arXiv1998

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.

hep-th↗