Seven-dimensional super Yang-Mills at negative coupling

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