TY - JOUR

T1 - Exact lattice supersymmetry

T2 - The two-dimensional [Formula Presented] Wess-Zumino model

AU - Catterall, Simon

AU - Karamov, Sergey

PY - 2002

Y1 - 2002

N2 - We study the two-dimensional Wess-Zumino model with extended (Formula presented) supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving exactly a single supersymmetric invariance at finite lattice spacing a. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to (Formula presented) where g is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the mass gaps in the boson and fermion sectors and to check the lattice Ward identities. At least for weak coupling we see no problems associated with a lack of reflection positivity in the lattice action and find good agreement with theory. At strong coupling we provide evidence that problems associated with a lack of reflection positivity are evaded for small enough lattice spacing.

AB - We study the two-dimensional Wess-Zumino model with extended (Formula presented) supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving exactly a single supersymmetric invariance at finite lattice spacing a. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to (Formula presented) where g is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the mass gaps in the boson and fermion sectors and to check the lattice Ward identities. At least for weak coupling we see no problems associated with a lack of reflection positivity in the lattice action and find good agreement with theory. At strong coupling we provide evidence that problems associated with a lack of reflection positivity are evaded for small enough lattice spacing.

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U2 - 10.1103/PhysRevD.65.094501

DO - 10.1103/PhysRevD.65.094501

M3 - Article

AN - SCOPUS:85038291959

SN - 1550-7998

VL - 65

SP - 10

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 9

ER -