Affiliation:
1. Uppsala University
2. Massachusetts Institute of Technology
Abstract
We consider the partition function for Euclidean
SU(N)SU(N)
super Yang-Mills on a squashed seven-sphere. We show that the
localization locus of the partition function has instanton membrane
solutions wrapping the six ``fixed" three-spheres on the
\mathbb{S}^7𝕊7.
The ADHM variables of these instantons are fields living on the membrane
world volume. We compute their contribution by localizing the resulting
three-dimensional supersymmetric field theory. In the round-sphere limit
the individual instanton contributions are singular, but the
singularities cancel when adding the contributions of all six
three-spheres. The full partition function on the
{\mathbb S}^7𝕊7
is well-defined even when the square of the effective Yang-Mills
coupling is negative. We show for an SU(2)SU(2)
gauge theory in this regime that the bare negative tension of the
instanton membranes is canceled off by contributions from the instanton
partition function, indicating the existence of tensionless membranes.
We provide evidence that this phase is distinct from the usual weakly
coupled super Yang-Mills and, in fact, is gravitational.
Funder
Knut och Alice Wallenbergs Stiftelse
National Science Foundation
Vetenskapsrådet
Subject
General Physics and Astronomy