Wilson renormalization group for supersymmetric gauge theories and gauge anomalies

Abstract

We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless Wess-Zumino model and deduce its perturbative expansion. We then consider N=1 supersymmetric Yang-Mills and show that the local gauge symmetry -broken by the regularization-can be recovered by a suitable choice of the RG flow boundary conditions. We restrict our analysis to the first loop, the generalization to higher loops presenting no difficulty due to the iterative nature of the procedure. Furthermore, adding matter fields, we reproduce the one-loop supersymmetric chiral anomaly to the second order in the vector field.

Aspects of the functional renormalisation group

“…The STI for the Schwinger functional (7.13) turns into [98][99][100][101][102][103][104][105][106][107][108][109][110][111][112][113][114][115] …”

N=1Wess-Zumino model ind=3at zero and finite temperature

“…Since (a 2 k→0 ) T =0 increases with increasing (a 2 Λ ) T =0 , the phase-transition temperature increases with increasing (a 2 k→0 ) T =0 , i. e. in terms of the renormalized quantity 11 . Our observation of an increasing phase-transition temperature with increasing (a 2 k→0 ) T =0 10 As initial conditions for the finite-temperature RG flows we use the zero-temperature values of the couplings (λ Λ , a 2 Λ ) at the cutoff scale. Therefore we have to restrict our study to temperatures significantly smaller than the UV cutoff in order to ensure that it is justified to use these zero-temperature values of the couplings at the UV starting point of the flow.…”

“…The delicate point here is, of course, the construction and use of a manifestly supersymmetry-preserving regulator. For the four-dimensional Wess-Zumino model such a regulator has been presented in [9,10]. Recently, general theories of a scalar superfield including the Wess-Zumino model have been investigated with a Polchinski-type RG equation in [11], yielding a new approach to supersymmetric nonrenormalization theorems.…”

Hard-soft renormalization of the massless Wess-Zumino model

“…It would be interesting to use this approach to study the massless Wess-Zumino model. A first step in this direction has been made in [22], where the flow equation has been written in the superfield formalism.…”