# Super Background Field Method for N=2 SYM

## Abstract

The implementation of the Background Field Method (BFM) for quantum field theories is analyzed within the Batalin-Vilkovisky (BV) formalism. We provide a systematic way of constructing general splittings of the fields into classical and quantum parts, such that the background transformations of the quantum fields are linear in the quantum variables. This leads to linear Ward-Takahashi identities for the background invariance and to great simplifications in multiloop computations. In addition, the gauge fixing is obtained by means of (anti)canonical transformations generated by the gauge-fixing fermion. Within this framework we derive the BFM for the N=2 Super-Yang-Mills theory in the Wess-Zumino gauge viewed as the twisted version of Donaldson-Witten topological gauge theory. We obtain the background transformations for the full BRST differential of N=2 Super-Yang-Mills (including gauge transformations, SUSY transformations and translations). The BFM permits all observables of the supersymmetric theory to be identified easily by computing the equivariant cohomology of the topological theory. These results should be regarded as a step towards the construction of a super BFM for the Minimal Supersymmetric Standard Model.

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center, Menlo Park, CA (US)

- Sponsoring Org.:
- USDOE Office of Science (US)

- OSTI Identifier:
- 815286

- Report Number(s):
- SLAC-PUB-9853

TRN: US0304576

- DOE Contract Number:
- AC03-76SF00515

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 12 Aug 2003

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CONSTRUCTION; FIELD THEORIES; GAUGE INVARIANCE; IMPLEMENTATION; STANDARD MODEL; TRANSFORMATIONS

### Citation Formats

```
Hurth, Tobias.
```*Super Background Field Method for N=2 SYM*. United States: N. p., 2003.
Web. doi:10.2172/815286.

```
Hurth, Tobias.
```*Super Background Field Method for N=2 SYM*. United States. https://doi.org/10.2172/815286

```
Hurth, Tobias. Tue .
"Super Background Field Method for N=2 SYM". United States. https://doi.org/10.2172/815286. https://www.osti.gov/servlets/purl/815286.
```

```
@article{osti_815286,
```

title = {Super Background Field Method for N=2 SYM},

author = {Hurth, Tobias},

abstractNote = {The implementation of the Background Field Method (BFM) for quantum field theories is analyzed within the Batalin-Vilkovisky (BV) formalism. We provide a systematic way of constructing general splittings of the fields into classical and quantum parts, such that the background transformations of the quantum fields are linear in the quantum variables. This leads to linear Ward-Takahashi identities for the background invariance and to great simplifications in multiloop computations. In addition, the gauge fixing is obtained by means of (anti)canonical transformations generated by the gauge-fixing fermion. Within this framework we derive the BFM for the N=2 Super-Yang-Mills theory in the Wess-Zumino gauge viewed as the twisted version of Donaldson-Witten topological gauge theory. We obtain the background transformations for the full BRST differential of N=2 Super-Yang-Mills (including gauge transformations, SUSY transformations and translations). The BFM permits all observables of the supersymmetric theory to be identified easily by computing the equivariant cohomology of the topological theory. These results should be regarded as a step towards the construction of a super BFM for the Minimal Supersymmetric Standard Model.},

doi = {10.2172/815286},

url = {https://www.osti.gov/biblio/815286},
journal = {},

number = ,

volume = ,

place = {United States},

year = {2003},

month = {8}

}