On instanton contributions to anomalous dimensions in N=4 supersymmetric YangMills theory
Abstract
Instanton contributions to the anomalous dimensions of gaugeinvariant composite operators in the N=4 supersymmetric SU( N) YangMills theory are studied in the oneinstanton sector. Independent sets of scalar operators of bare dimension ∆_{0}⩽5 are constructed in all the allowed representations of the SU(4) Rsymmetry group and their twopoint functions are computed in the semiclassical approximation. Analysing the moduli space integrals the sectors in which the scaling dimensions receive nonperturbative contributions are identified. The requirement that the integrations over the fermionic collective coordinates which arise in the instanton background are saturated leads to nonrenormalisation properties for a large class of operators. Instantoninduced 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 nonrenormalisation 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.
 Publication:

Nuclear Physics B
 Pub Date:
 April 2004
 DOI:
 10.1016/j.nuclphysb.2004.02.014
 arXiv:
 arXiv:hepth/0310193
 Bibcode:
 2004NuPhB.684....3K
 Keywords:

 11.15.Tk;
 11.30.Pb;
 12.60.Jv;
 Other nonperturbative techniques;
 Supersymmetry;
 Supersymmetric models;
 High Energy Physics  Theory
 EPrint:
 LaTeX, 71 pages, no figures