Real versus complex β-deformation of the 𝒩 = 4 planar super Yang-Mills theory

Abstract

This is a sequel of our paper hep-th/0606125 in which we have studied the N = 1 SU(N) SYM theory obtained as a marginal deformation of the N = 4 theory, with a complex deformation parameter β and in the planar limit. There we have addressed the issue of conformal invariance imposing the theory to be finite and we have found that finiteness requires reality of the deformation parameter β. In this paper we relax the finiteness request and look for a theory that in the planar limit has vanishing beta functions. We perform explicit calculations up to five loop order: we find that the conditions of beta function vanishing can be achieved with a complex deformation parameter, but the theory is not finite and the result depends on the arbitrary choice of the subtraction procedure. Therefore, while the finiteness condition leads to a scheme independent result, so that the conformal invariant theory with a real deformation is physically well defined, the condition of vanishing beta function leads to a result which is scheme dependent and therefore of unclear significance. In order to show that these findings are not an artefact of dimensional regularization, we confirm our results within the differential renormalization approach.

Giant gravitons and the emergence of geometric limits in β-deformations of N = 4 $$ \mathcal{N}=4 $$ SYM

“…This can be conveniently understood by noticing that the corresponding spin chain can be obtained by twisting the original spin chain of N = 4 SYM theory [11]. Results to various loop orders when |h| = 1 were obtained in [39]. At one loop order one has that g 2 Y M (1 + |h| 2 ) = 2G 2 Y M .…”

Bilocal phase operators inβ-deformed super Yang-Mills

“…Marginal deformations of conformally invariant supersymmetric gauge theories were first systematically studied by Leigh and Strassler [17], and have subsequently been analyzed extensively both perturbatively and at strong coupling in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] just to mention a few.…”

Dynamical SUSY breaking and the β-deformation

“…There is a large debate in the literature on the finiteness request and the conformal invariance of the complex beta deformation [20]. Here we just require that the theory is conformal if the beta functions of the coupling constants are vanishing and we do not worry about the finiteness problem associated to the deformation.…”