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Seven-dimensional super Yang-Mills at negative coupling

by Joseph A. Minahan, Usman Naseer, Charles Thull

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Submission summary

Authors (as registered SciPost users): Usman Naseer · Charles Thull
Submission information
Preprint Link: https://arxiv.org/abs/2208.01115v3  (pdf)
Date accepted: 2022-10-03
Date submitted: 2022-09-29 11:54
Submitted by: Thull, Charles
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory

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 $\mathbb{S}^7$. 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 ${\mathbb S}^7$ is well-defined even when the square of the effective Yang-Mills 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 Yang-Mills and, in fact, is gravitational.

Author comments upon resubmission

We thank the referees for their careful reading of the manuscript. We have included all of their suggestions in the new manuscript, a list of all the changes is given.

List of changes

1. Before eq. (2.6) added \kappa\wedge to \iota_v F
2. Before eq. (2.8) “\hat F^+ decompose” changed to “\hat F^+ decomposes”
3. eq. (2.9) and (2.11) added delta functions to make it SU(N) partition functions
4. after (2.25) deleted one “equals”
5. after (2.31) changed “expressed” to “suppressed”
6. before (3.1) changed “Localizing” to “localizing”
7. after (3.1) changed “i_v F” to “\iota_v F”
8. after (3.2) added the definition of \varrho_5
9. before (3.9) changed “the two eigenvalues are widely separated” to “the eigenvalue $\sigma_1=-\sigma_2$ is large”
10. after (3.10) changed “where the last step […]” to “where we have again expanded around the saddle point $\sigma_{12}=-\frac{4\pi^2\mathcal{R}}{g_{YM}^2}$ in the small negative $g_{YM}^2$ limit. The last step [...]”
11. in (3.12) changed = to \approx
12. after (3.13) in the definition of q changed \omega_2 to \omega_1
13. before (4.1) removed one “given”
14. In (4.1) changed k to \kappa
15. before (4.14) added the article to “the dominant contribution”
16. in (B.20) changed “j\neq x” to “i\neq x”
17. Figure 2(a) exchanged “\hat{m}-1” and “\hat{n}-1”

Published as SciPost Phys. 14, 028 (2023)

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