Authors construct supersymmetric embeddings for non-SUSY gauge theory operators up to dimension six and use vector bundles to reveal an underlying complex geometry that organizes operators under field redefinitions across spins.
One-loop non-renormalization results in EFTs
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abstract
In Effective Field Theories (EFTs) with higher-dimensional operators many anomalous dimensions vanish at the one-loop level for no apparent reason. With the use of supersymmetry, and a classification of the operators according to their embedding in super-operators, we are able to show why many of these anomalous dimensions are zero. The key observation is that one-loop contributions from superpartners trivially vanish in many cases under consideration, making supersymmetry a powerful tool even for non-supersymmetric models. We show this in detail in a simple U(1) model with a scalar and fermions, and explain how to extend this to SM EFTs and the QCD Chiral Langrangian. This provides an understanding of why most "current-current" operators do not renormalize "loop" operators at the one-loop level, and allows to find the few exceptions to this ubiquitous rule.
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Supersymmetric geometry in non-supersymmetric effective field theory
Authors construct supersymmetric embeddings for non-SUSY gauge theory operators up to dimension six and use vector bundles to reveal an underlying complex geometry that organizes operators under field redefinitions across spins.