Supersymmetric gradient flow in N=1 SYM

The gradient flow equation is derived in N=1 supersymmetric Yang-Mills theory in terms of the component field of the Wess-Zumino gauge. We show that the flow-time derivative and supersymmetry transformation that is naively extended to five dimensions commute with each other up to a gauge transformation. In this sense, the obtained flow is supersymmetric in the Wess-Zumino gauge. We also discuss more about the symmetry of the flow equation.Comment: 24 page

Supersymmetric gradient flow in 4d N=1 SQCD

A supersymmetric gradient flow for four-dimensional N=1 supersymmetric QCD (SQCD) is proposed. The flow equation is given in both the superfield and component fields of the Wess-Zumino gauge. The superfield flow equation is defined for each of the gauge and matter multiplets individually. Adding a gauge fixing, the component-field flow equation is defined in the Wess-Zumino gauge in a gauge covariant manner. We find that the latter equation is supersymmetric in a sense that the commutator of the flow time derivative and the supersymmetry transformation vanishes up to a gauge transformation. We also discuss a simplified flow by using the gradient of supersymmetric Yang-Mills (SYM) action instead of using SQCD action to define a gauge multiplet flow.Comment: 5 page

Towards the Super Yang-Mills Theory on the Lattice

We present an entirely new approach towards a realization of the supersymmetric Yang-Mills theory on the lattice. The action consists of the staggered fermion and the plaquette variables distributed in the Euclidean space with a particular pattern. The system is shown to have fermionic symmetries relating the fermion and the link variables.Comment: 12 pages, 3 figure

Perturbative analysis of the Wess-Zumino flow

We investigate an interacting supersymmetric gradient flow in the Wess-Zumino model. Thanks to the non-renormalization theorem and an appropriate initial condition, we find that any correlator of flowed fields is ultraviolet finite. This is shown at all orders of the perturbation theory using the power counting theorem for 1PI supergraphs. Since the model does not have the gauge symmetry, the mechanism of realizing the ultraviolet finiteness is quite different from that of the Yang-Mills flow, and this could provide further understanding of the gradient flow approach.Comment: 30 pages, 2 figure