1202.2598 (Hiroshi Suzuki)

Supersymmetry, chiral symmetry and the generalized BRS transformation in
lattice formulations of 4D $\mathcal{N}=1$ SYM    [PDF]

Hiroshi Suzuki

In the context of the lattice regularization of the four-dimensional
$\mathcal{N}=1$ supersymmetric Yang--Mills theory (4D $\mathcal{N}=1$ SYM), we
formulate a generalized BRS transformation that treats the gauge, supersymmetry
(SUSY), translation and $U(1)_A$ transformations in a unified way. A resultant
Slavnov--Taylor identity or the Zinn-Justin equation gives rise to a strong
constraint on the quantum continuum limit of symmetry breaking terms with the
lattice regularization. By analyzing the implications of the constraint on
operator-mixing coefficients in the SUSY and the $U(1)_A$ Ward--Takahashi (WT)
identities, we prove to all orders of perturbation theory in the continuum
limit that, (i) the chiral symmetric limit implies the supersymmetric limit
and, (ii) a three-fermion operator that might potentially give rise to an
exotic breaking of the SUSY WT identity does not emerge. In previous
literature, only a naive or incomplete treatment on these points can be found.
Our results provide a solid theoretical basis for lattice formulations of the
4D $\mathcal{N}=1$ SYM.

View original: http://arxiv.org/abs/1202.2598