Quantum Effects in Supersymmetric Galilean Yang-Mills

Abstract

We study the quantum dynamics of supersymmetric Galilean Yang-Mills (SGYM), with a focus on three dimensions where there is a classical scale symmetry. This is believed to be the worldvolume theory describing D2-branes within type IIA non-relativistic string theory and arises as a non-relativistic limit of maximally supersymmetric (relativistic) Yang-Mills. Unlike the relativistic case, we find that SGYM only admits perturbative dynamical excitations on the Coulomb branch. We show that in three dimensions the classical scale symmetry is broken at one-loop due to logarithmic divergences which cannot be absorbed by renormalization of existing couplings. As such we find that SGYM is non-renormalizable. However, we argue that by including additional marginal deformations the original coupling can be renormalized and rendered asymptotically free. Finally, we propose that three-dimensional SGYM flows to a strongly coupled non-relativistic M2-brane theory.

arXiv comment55 pages, 1 figure, v2: Added references, improved clarity of text, typos corrected, version accepted for publication in JHEP