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Supersymmetry on a Euclidean Spacetime Lattice I: A Target Theory with Four Supercharges

Andrew G. Cohen, David B. Kaplan, Emanuel Katz, Mithat Unsal

Abstract

We formulate a Euclidean spacetime lattice whose continuum limit is (2,2) supersymmetric Yang-Mills theory in two dimensions, a theory which possesses four supercharges and an anomalous global chiral symmetry. The lattice action respects one exact supersymmetry, which allows the target theory to emerge in the continuum limit without fine-tuning. Our method exploits an orbifold construction described previously for spatial lattices in Minkowski space, and can be generalized to more complicated theories with additional supersymmetry and more spacetime dimensions.

Supersymmetry on a Euclidean Spacetime Lattice I: A Target Theory with Four Supercharges

Abstract

We formulate a Euclidean spacetime lattice whose continuum limit is (2,2) supersymmetric Yang-Mills theory in two dimensions, a theory which possesses four supercharges and an anomalous global chiral symmetry. The lattice action respects one exact supersymmetry, which allows the target theory to emerge in the continuum limit without fine-tuning. Our method exploits an orbifold construction described previously for spatial lattices in Minkowski space, and can be generalized to more complicated theories with additional supersymmetry and more spacetime dimensions.

Paper Structure

This paper contains 12 sections, 60 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction and results
  2. Constructing the lattice action
  3. Symmetries of the lattice action
  4. The $U(k)$ gauge symmetry
  5. The $Z_N\times Z_N$ translation symmetry
  6. The $U(1)^3$ global symmetry
  7. The $Z_2$ point group
  8. The ${\cal Q}=1$ supersymmetry and a superfield formulation
  9. The continuum limit: tree level
  10. The continuum limit: renormalization
  11. Moduli
  12. Discussion

Figures (1)

  • Figure 1: The two dimensional Euclidean lattice for the two dimensional SYM theory with four supercharges. The lattice respects one exact supercharge. Arrows on the links signify the orientation of the $\mathbf{r}$ charge vectors of the link fermions, as discussed in §2.