SciPost Submission Page
Seven-dimensional super Yang-Mills at negative coupling
by Joseph A. Minahan, Usman Naseer, Charles Thull
This Submission thread is now published as
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: |
|
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
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)