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Title: On the Noncommutativity Approach to Supersymmetry on the Lattice

Abstract

The noncommutativity approach to SUSY on the lattice is shown to be inconsistent and a similar inconsistency is displayed for the link approach.

Authors:
 [1];  [2]
  1. Institut fuer Theoretische Physik, Universitaet Regensburg, D-93040 Regensburg (Germany)
  2. Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, NL-2300 RA Leiden (Netherlands)
Publication Date:
OSTI Identifier:
21056796
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 892; Journal Issue: 1; Conference: QCHS7: 7. conference on quark confinement and the hadron spectrum, Ponta Delgada, Acores (Portugal), 2-7 Sep 2006; Other Information: DOI: 10.1063/1.2714361; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMMUTATION RELATIONS; LATTICE FIELD THEORY; SPARTICLES; STANDARD MODEL; SUPERSYMMETRY

Citation Formats

Bruckmann, Falk, and Kok, Mark de. On the Noncommutativity Approach to Supersymmetry on the Lattice. United States: N. p., 2007. Web. doi:10.1063/1.2714361.
Bruckmann, Falk, & Kok, Mark de. On the Noncommutativity Approach to Supersymmetry on the Lattice. United States. doi:10.1063/1.2714361.
Bruckmann, Falk, and Kok, Mark de. Tue . "On the Noncommutativity Approach to Supersymmetry on the Lattice". United States. doi:10.1063/1.2714361.
@article{osti_21056796,
title = {On the Noncommutativity Approach to Supersymmetry on the Lattice},
author = {Bruckmann, Falk and Kok, Mark de},
abstractNote = {The noncommutativity approach to SUSY on the lattice is shown to be inconsistent and a similar inconsistency is displayed for the link approach.},
doi = {10.1063/1.2714361},
journal = {AIP Conference Proceedings},
number = 1,
volume = 892,
place = {United States},
year = {Tue Feb 27 00:00:00 EST 2007},
month = {Tue Feb 27 00:00:00 EST 2007}
}
  • It is argued that the noncommutativity approach to fully supersymmetric field theories on the lattice suffers from an inconsistency. Supersymmetric quantum mechanics is worked out in this formalism and the inconsistency is shown both in general and explicitly for that system, as well as for the Abelian super BF model.
  • We construct a cubic lattice of discrete points in superspace, as well as a discrete subgroup of the supersymmetry group which maps this ''superlattice'' into itself. We discuss the connection between this structure and previous versions of lattice supersymmetry. Our approach clarifies the mathematical problems of formulating supersymmetric lattice field theories and suggests new methods for attacking them.
  • We examine the link approach to constructing a lattice theory of N=2 super Yang-Mills theory in two dimensions. The goal of this construction is to provide a discretization of the continuum theory which preserves all supersymmetries at nonzero lattice spacing. We show that this approach suffers from an inconsistency and argue that a maximum of just one of the supersymmetries can be implemented on the lattice.
  • A manifestly supersymmetric nonperturbative matrix regularization for a twisted version of N = (8, 8) theory on a curved background (a two-sphere) is constructed. Both continuum and the matrix regularization respect four exact scalar supersymmetries under a twisted version of the supersymmetry algebra. We then discuss a succinct Q = 1 deformed matrix model regularization of N = 4 SYM in d = 4, which is equivalent to a non-commutative A*{sub 4} orbifold lattice formulation. Motivated by recent progress in supersymmetric lattices, we also propose a N = 1/4 supersymmetry preserving deformation of N = 4 SYM theory on R{supmore » 4}. In this class of N = 1/4 theories, both the regularized and continuum theory respect the same set of (scalar) supersymmetry. By using the equivalence of the deformed matrix models with the lattice formulations, we give a very simple physical argument on why the exact lattice supersymmetry must be a subset of scalar subalgebra. This argument disagrees with the recent claims of the link approach, for which we give a new interpretation.« less
  • We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.