### Abstract

We discuss a new approach to putting supersymmetric theories on the lattice. The basic idea is to start from a twisted formulation of the underlying supersymmetric theory in which the fermions are represented as grassmann valued antisymmetric tensor fields. The original supersymmetry algebra is replaced by a twisted algebra which contains a scalar nilpotent supercharge Q. Furthermore the action of the theory can then be written as the Q-variation of some function. The case of N = 2 super Yang-Mills theory in two dimensions is discussed in some detail. We then present our proposal for discretizing this theory and derive the resultant lattice action. The latter is local, free of spectrum doubling, gauge invariant and preserves the scalar supercharge invariance exactly. Some preliminary numerical results are then presented. The approach can be naturally generalized to yield a lattice action for N = 4 super Yang-Mills in four dimensions.

Original language | English (US) |
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Journal | Proceedings of Science |

Volume | 20 |

State | Published - Jan 1 2005 |

Event | 23rd International Symposium on Lattice Field Theory, LAT 2005 - Dublin, Ireland Duration: Jul 25 2005 → Jul 30 2005 |

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### ASJC Scopus subject areas

- General

### Cite this

**Dirac-Kähler fermions and exact lattice supersymmetry.** / Catterall, Simon M.

Research output: Contribution to journal › Conference article

}

TY - JOUR

T1 - Dirac-Kähler fermions and exact lattice supersymmetry

AU - Catterall, Simon M

PY - 2005/1/1

Y1 - 2005/1/1

N2 - We discuss a new approach to putting supersymmetric theories on the lattice. The basic idea is to start from a twisted formulation of the underlying supersymmetric theory in which the fermions are represented as grassmann valued antisymmetric tensor fields. The original supersymmetry algebra is replaced by a twisted algebra which contains a scalar nilpotent supercharge Q. Furthermore the action of the theory can then be written as the Q-variation of some function. The case of N = 2 super Yang-Mills theory in two dimensions is discussed in some detail. We then present our proposal for discretizing this theory and derive the resultant lattice action. The latter is local, free of spectrum doubling, gauge invariant and preserves the scalar supercharge invariance exactly. Some preliminary numerical results are then presented. The approach can be naturally generalized to yield a lattice action for N = 4 super Yang-Mills in four dimensions.

AB - We discuss a new approach to putting supersymmetric theories on the lattice. The basic idea is to start from a twisted formulation of the underlying supersymmetric theory in which the fermions are represented as grassmann valued antisymmetric tensor fields. The original supersymmetry algebra is replaced by a twisted algebra which contains a scalar nilpotent supercharge Q. Furthermore the action of the theory can then be written as the Q-variation of some function. The case of N = 2 super Yang-Mills theory in two dimensions is discussed in some detail. We then present our proposal for discretizing this theory and derive the resultant lattice action. The latter is local, free of spectrum doubling, gauge invariant and preserves the scalar supercharge invariance exactly. Some preliminary numerical results are then presented. The approach can be naturally generalized to yield a lattice action for N = 4 super Yang-Mills in four dimensions.

UR - http://www.scopus.com/inward/record.url?scp=84856126540&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856126540&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:84856126540

VL - 20

JO - Proceedings of Science

JF - Proceedings of Science

SN - 1824-8039

ER -