# Spectral sum rules for confining large-N theories

## Abstract

We consider asymptotically-free four-dimensional large-$N$ gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large-$N$ confined-phase spectral sums. The analysis is done in the limit of vanishing ’t Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale Λ ^{₋1}. We find our results motivate us to conjecture some universal spectral sum rules for these large $N$ gauge theories.

- Authors:

- Univ. of Washington, Seattle, WA (United States). Inst. for Nuclear Theory
- Univ. of Tokyo, Chiba (Japan); Univ. of Copenhagen (Denmark). The Niels Bohr International Academy & Discovery Center
- Univ. of Tokyo, Chiba (Japan); ; Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

- Publication Date:

- Research Org.:
- Univ. of Washington, Seattle, WA (United States)

- Sponsoring Org.:
- USDOE; Japan Society for the Promotion of Science (JSPS); National Science Foundation (NSF)

- OSTI Identifier:
- 1326998

- Grant/Contract Number:
- FG02-00ER41132; PHYS-1066293; 15K17634

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 6; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Confinement; 1/N Expansion

### Citation Formats

```
Cherman, Aleksey, McGady, David A., and Yamazaki, Masahito.
```*Spectral sum rules for confining large-N theories*. United States: N. p., 2016.
Web. doi:10.1007/JHEP06(2016)095.

```
Cherman, Aleksey, McGady, David A., & Yamazaki, Masahito.
```*Spectral sum rules for confining large-N theories*. United States. doi:10.1007/JHEP06(2016)095.

```
Cherman, Aleksey, McGady, David A., and Yamazaki, Masahito. Fri .
"Spectral sum rules for confining large-N theories". United States.
doi:10.1007/JHEP06(2016)095. https://www.osti.gov/servlets/purl/1326998.
```

```
@article{osti_1326998,
```

title = {Spectral sum rules for confining large-N theories},

author = {Cherman, Aleksey and McGady, David A. and Yamazaki, Masahito},

abstractNote = {We consider asymptotically-free four-dimensional large-$N$ gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large-$N$ confined-phase spectral sums. The analysis is done in the limit of vanishing ’t Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale Λ₋1. We find our results motivate us to conjecture some universal spectral sum rules for these large $N$ gauge theories.},

doi = {10.1007/JHEP06(2016)095},

journal = {Journal of High Energy Physics (Online)},

number = 6,

volume = 2016,

place = {United States},

year = {Fri Jun 17 00:00:00 EDT 2016},

month = {Fri Jun 17 00:00:00 EDT 2016}

}

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