### Abstract

We propose a discretization of two dimensional euclidean Yang-Mills theories with N = 2 supersymmetry which preserves exactly both gauge invariance and an element of supersymmetry. The approach starts from the twisted form of the continuum super Yang Mills action which we show may be written in terms of two real Kähler-Dirac fields whose components transform into each other under the twisted supersymmetry. Once the theory is written in this geometrical language it is straightforward to discretize by mapping the component tensor fields to appropriate geometrical structures in the lattice and by replacing the continuum exterior derivative and its adjoint by appropriate lattice covariant difference operators. The lattice action is local and possesses a unique vacuum state while the use of Kähler-Dirac fermions ensures the model does not exhibit spectrum doubling.

Original language | English (US) |
---|---|

Pages (from-to) | 191-206 |

Number of pages | 16 |

Journal | Journal of High Energy Physics |

Volume | 8 |

Issue number | 11 |

State | Published - Nov 1 2004 |

### Fingerprint

### Keywords

- Extended Supersymmetry
- Lattice Gauge Field Theories
- Topological Field Theories

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**A geometrical approach to N = 2 super Yang-Mills theory on the two dimensional lattice.** / Catterall, Simon M.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 8, no. 11, pp. 191-206.

}

TY - JOUR

T1 - A geometrical approach to N = 2 super Yang-Mills theory on the two dimensional lattice

AU - Catterall, Simon M

PY - 2004/11/1

Y1 - 2004/11/1

N2 - We propose a discretization of two dimensional euclidean Yang-Mills theories with N = 2 supersymmetry which preserves exactly both gauge invariance and an element of supersymmetry. The approach starts from the twisted form of the continuum super Yang Mills action which we show may be written in terms of two real Kähler-Dirac fields whose components transform into each other under the twisted supersymmetry. Once the theory is written in this geometrical language it is straightforward to discretize by mapping the component tensor fields to appropriate geometrical structures in the lattice and by replacing the continuum exterior derivative and its adjoint by appropriate lattice covariant difference operators. The lattice action is local and possesses a unique vacuum state while the use of Kähler-Dirac fermions ensures the model does not exhibit spectrum doubling.

AB - We propose a discretization of two dimensional euclidean Yang-Mills theories with N = 2 supersymmetry which preserves exactly both gauge invariance and an element of supersymmetry. The approach starts from the twisted form of the continuum super Yang Mills action which we show may be written in terms of two real Kähler-Dirac fields whose components transform into each other under the twisted supersymmetry. Once the theory is written in this geometrical language it is straightforward to discretize by mapping the component tensor fields to appropriate geometrical structures in the lattice and by replacing the continuum exterior derivative and its adjoint by appropriate lattice covariant difference operators. The lattice action is local and possesses a unique vacuum state while the use of Kähler-Dirac fermions ensures the model does not exhibit spectrum doubling.

KW - Extended Supersymmetry

KW - Lattice Gauge Field Theories

KW - Topological Field Theories

UR - http://www.scopus.com/inward/record.url?scp=22144453715&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22144453715&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:22144453715

VL - 8

SP - 191

EP - 206

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 11

ER -