City Research Online

Abstract

We consider the partition function for Euclidean 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 S7. 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 S7 is well-defined even when the square of the effective YangMills coupling is negative. We show for an 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 YangMills and, in fact, is gravitational.

Publication Type:	Article
Additional Information:	This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.
Subjects:	Q Science > QC Physics
Departments:	School of Science & Technology School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

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