Maximal super Yang-Mills theories on curved background with off-shell supercharges

Abstract

We construct d ≤ 7 dimensional maximally supersymmetric Yang-Mills theories on a class of curved backgrounds with off-shell supercharges. The off-shell supersymmetry is mainly a generalization of on-shell supersymmetry previously constructed by Blau. We present several examples of backgrounds and discuss the number of the preserved supersymmetries on these backgrounds. We also construct another maximally supersymmetric Yang-Mills theories on S 3 obtained by dimensional reduction along R-direction of N = 4 super Yang-Mills theory on R × S 3 .

Gauge theories with 16 supersymmetries on spheres

“…However, the AB combination has a leftover piece 15) where ε 890 = 1. This term can be canceled by including the extra term in the Lagrangian…”

“…A Euclidean version of this was done for the maximally supersymmetric case in [15]. An offshell formulation does not exist for all 16 supersymmetries, but it is only necessary to go offshell for one particular ǫ.…”

“…This is accomplished in a way that parallels Pestun's analysis [1], although we give a somewhat simpler method. Effectively, D 10 appears in the expression 15) where the primed indices exclude the 0 component and the terms involving the ghost fields fix the gauge. Since the ellipticity of an operator is determined by its symbol S, we only need consider the leading derivatives, where we replace all ∇ µ with p µ .…”

“…The log of the infinite product is logarithmically divergent, and thus requires regularization. As before we can regularize the product by introducing a cut-off for the modes n 0 = Λr in the divergent part and absorb this divergent part by an appropriate redefinition of the coupling constant 15) where g 0 is the bare coupling and γ is the Euler constant. From now on we assume that the product is regularized and the divergence is absorbed into the Yang-Mills coupling.…”

Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions

“…Of all the bosonic supersymmetric conformal supergravity backgrounds the Yang-Mills supermultiplet above can be defined upon, the maximally supersymmetric AdS 3 × S 7 and AdS 7 × S 3 Freund-Rubin backgrounds classified in section 2.4 are perhaps the most compelling. In particular, it would interesting to explore whether the Yang-Mills supermultiplet on these conformal supergravity backgrounds admits a consistent truncation that would recover one of the theories described in [13,22,24,76,92]. The relevant theories in [13] (or [24]) would follow by dimensionally reducing the on-shell (or partially off-shell) Yang-Mills supermultiplet on R 9,1 to some lower dimension d equal to either 7 or 3, before deforming the resulting supermultiplet in dimension d in such a way that it retains rigid supersymmetry on a curved space admitting the maximum number of real or imaginary Killing spinors, i.e., either AdS d or S d .…”