TY - JOUR

T1 - Lattice supersymmetry and topological field theory

AU - Catterall, Simon

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2003/5/1

Y1 - 2003/5/1

N2 - It is known that certain theories with extended supersymmetry can be discretized in such a way as to preserve an exact fermionic symmetry. In the simplest model of this kind, we show that this residual supersymmetric invariance is actually a BRST symmetry associated with gauge fixing an underlying local shift symmetry. Furthermore, the original lattice action is then seen to be entirely a gauge fixing term. The corresponding continuum theory has a topological field theory interpretation. We look, in detail, at one example - supersymmetric quantum mechanics which possesses two such BRST symmetries. In this case, we show that the lattice theory can be obtained by blocking out of the continuum in a carefully chosen background metric. Such a procedure will not change the Ward identities corresponding to the BRST symmetries since they correspond to topological observables. Thus, at the quantum level, the continuum BRST symmetry is preserved in the lattice theory. Similar conclusions are reached for the two-dimensional complex Wess-Zumino model and imply that all the supersymmetric Ward identities are satisfied exactly on the lattice. Numerical results supporting these conclusions are presented.

AB - It is known that certain theories with extended supersymmetry can be discretized in such a way as to preserve an exact fermionic symmetry. In the simplest model of this kind, we show that this residual supersymmetric invariance is actually a BRST symmetry associated with gauge fixing an underlying local shift symmetry. Furthermore, the original lattice action is then seen to be entirely a gauge fixing term. The corresponding continuum theory has a topological field theory interpretation. We look, in detail, at one example - supersymmetric quantum mechanics which possesses two such BRST symmetries. In this case, we show that the lattice theory can be obtained by blocking out of the continuum in a carefully chosen background metric. Such a procedure will not change the Ward identities corresponding to the BRST symmetries since they correspond to topological observables. Thus, at the quantum level, the continuum BRST symmetry is preserved in the lattice theory. Similar conclusions are reached for the two-dimensional complex Wess-Zumino model and imply that all the supersymmetric Ward identities are satisfied exactly on the lattice. Numerical results supporting these conclusions are presented.

KW - Extended Supersymmetry

KW - Lattice Quantum Field Theory

KW - Topological Field Theories

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U2 - 10.1088/1126-6708/2003/05/038

DO - 10.1088/1126-6708/2003/05/038

M3 - Article

AN - SCOPUS:23044462183

VL - 7

SP - 843

EP - 862

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 5

ER -