Gauge Coupling Field, Currents, Anomalies and N=1 Super-Yang-Mills Effective Actions

TL;DR

This paper constructs all-order effective actions for N=1 super-Yang-Mills theory using a gauge coupling superfield, anomaly matching, and superspace identities, deriving the NSVZ beta function algebraically.

Contribution

It introduces a fully compatible effective Lagrangian framework for super-Yang-Mills, incorporating anomalies and deriving the NSVZ beta function algebraically.

Findings

Derived the Wilsonian effective Lagrangian using anomaly matching.

Obtained the effective action for gaugino condensates as a function of the coupling.

Provided algebraic derivation of the NSVZ beta function.

Abstract

Working with a gauge coupling field in a linear superfield, we construct effective Lagrangians for N=1 super-Yang-Mills theory fully compatible with the expected all-order behaviour or physical quantities. Using the one-loop dependence on its ultraviolet cutoff and anomaly matching or cancellation of R and dilatation anomalies, we obtain the Wilsonian effective Lagrangian. With similar anomaly matching or cancellation methods, we derive the effective action for gaugino condensates, as a function of the real coupling field. Both effective actions lead to a derivation of the NSVZ beta function from algebraic arguments only. The extension of results to N=2 theories or to matter systems is briefly considered. The main tool for the discussion of anomalies is a generic supercurrent structure with 16_B+16_F operators (the S multiplet), which we derive using superspace identities and field equations for a fully general gauge theory Lagrangian with the linear gauge coupling superfield, and with various U(1)_R currents. As a byproduct, we show under which conditions the S multiplet can be improved to contain the Callan-Coleman-Jackiw energy-momentum tensor whose trace measures the breaking of scale invariance.