# The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

## Abstract

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics — which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription — to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of themore »

- Authors:

- Univ. of Cincinnati, OH (United States)
- San Francisco State Univ., CA (United States). Dept Physics & Astronomy; SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1362077

- Report Number(s):
- SLAC-PUB-16996

Journal ID: ISSN 1029-8479; arXiv:1206.1890

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 2012; Journal Issue: 8; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Theory-HEP; ASTRO; HEPTH

### Citation Formats

```
Argyres, Philip C., and Uensal, Mithat.
```*The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects*. United States: N. p., 2012.
Web. doi:10.1007/JHEP08(2012)063.

```
Argyres, Philip C., & Uensal, Mithat.
```*The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects*. United States. doi:10.1007/JHEP08(2012)063.

```
Argyres, Philip C., and Uensal, Mithat. Fri .
"The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects". United States. doi:10.1007/JHEP08(2012)063. https://www.osti.gov/servlets/purl/1362077.
```

```
@article{osti_1362077,
```

title = {The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects},

author = {Argyres, Philip C. and Uensal, Mithat},

abstractNote = {We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics — which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription — to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion-anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Écalle’s resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.},

doi = {10.1007/JHEP08(2012)063},

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

issn = {1029-8479},

number = 8,

volume = 2012,

place = {United States},

year = {2012},

month = {8}

}

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