Abstract
We clarify the structure of the four-dimensional low-energy effective action that encodes the conformal and U(1) R-symmetry anomalies in an \( \mathcal{N} \) = 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 [1] 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 \( \mathcal{N} \) = 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.
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ArXiv ePrint: 1312.2925
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Bobev, N., Elvang, H. & Olson, T.M. Dilaton effective action with \( \mathcal{N} \) = 1 supersymmetry. J. High Energ. Phys. 2014, 157 (2014). https://doi.org/10.1007/JHEP04(2014)157
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DOI: https://doi.org/10.1007/JHEP04(2014)157