Gauge coupling field, currents, anomalies and N=1 super-Yang–Mills effective actions

Ambrosetti, Nicola; Arnold, Daniel; Derendinger, Jean-Pierre; Hartong, Jelle (2017). Gauge coupling field, currents, anomalies and N=1 super-Yang–Mills effective actions. Nuclear physics. B, 915, pp. 285-334. Elsevier 10.1016/j.nuclphysb.2016.12.011

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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 behavior 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 β 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 16B+16F 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.

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