Generalisations of the Ginsparg-Wilson relation and a remnant of supersymmetry on the lattice
We introduce a lattice symmetry relation for field theories with general linear symmetries. For chiral symmetry the well-known Ginsparg-Wilson relation is reproduced. The new relation encodes the remnant of the original symmetry on the lattice and guides the construction of invariant lattice actions...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
2008
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| In: |
Arxiv
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| Online Access: | Verlag, kostenfrei, Volltext: http://arxiv.org/abs/0810.3547
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| Author Notes: | Georg Bergner,Theoretisch-Physikalisches Institut, Universität Jena, D-07743 Jena, Germany; Falk Bruckmann, Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany; Jan M. Pawlowski, Institut für Theoretische Physik, Universität Heidelberg, D-69120 Heidelberg, Germany |
| Summary: | We introduce a lattice symmetry relation for field theories with general linear symmetries. For chiral symmetry the well-known Ginsparg-Wilson relation is reproduced. The new relation encodes the remnant of the original symmetry on the lattice and guides the construction of invariant lattice actions. We apply this approach to lattice supersymmetry. There, an additional constraint has to be satisfied which originates in the derivative operator in the symmetry transformations. As a consequence the non-local SLAC derivative operator appears in the lattice transformation. Despite this non-local form we show how local solutions for quadratic actions can be found. For interacting theories the relation in general leads to a non-polynomial action that can be reduced to a finite polynomial order only under certain conditions. |
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| Item Description: | Gesehen am 05.12.2017 |
| Physical Description: | Online Resource |