2013/12/10 by Nikolay Bobev, Henriette Elvang, Timothy M. Olson
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep04(2014)157
published as JHEP 1404 (2014) 157 · 18 pages
arxiv created 2013/12/10 · arxiv updated 2015/06/18
We clarify the structure of the four-dimensional low-energy effective action that encodes the conformal and U(1) R-symmetry anomalies in an N=1 supersymmetric field theory. The action depends on the dilaton, τ, associated with broken conformal symmetry, and the Goldstone mode, β, of the broken U(1) R-symmetry. We present the action for general curved spacetime and background gauge field up to and including all possible four-derivative terms. The result, constructed from basic principles, extends and clarifies the structure found by Schwimmer and Theisen in arXiv:1011.0696 using superfield methods. We show that the Goldstone mode β does not interfere with the proof of the four-dimensional a-theorem based on 2 → 2 dilaton scattering. In fact, supersymmetry Ward identities ensure that a proof of the a-theorem can also be based on 2 → 2 Goldstone mode scattering when the low-energy theory preserves N=1 supersymmetry. We find that even without supersymmetry, a Goldstone mode for any broken global U(1) symmetry cannot interfere with the proof of the four-dimensional a-theorem.