Shortening Anomalies in Supersymmetric Theories

Abstract

We present new anomalies in two-dimensional $\mathcal{N}=(2,2)$ superconformal theories. They obstruct the shortening conditions of chiral and twisted chiral multiplets at coincident points. This implies that marginal couplings cannot be promoted to background superfields in short representations. Therefore, standard results that follow from $\mathcal{N}=(2,2)$ spurion analysis are invalidated. These anomalies appear only if supersymmetry is enhanced beyond $\mathcal{N}=(2,2)$. These anomalies explain why the conformal manifolds of the K3 and $T^4$ sigma models are not Kähler and do not factorize into chiral and twisted chiral moduli spaces and why there are no $\mathcal{N}=(2,2)$ gauged linear sigma models that cover these conformal manifolds. We also present these results from the point of view of the Riemann curvature of conformal manifolds.

arXiv comment31 pages. v2: reference added

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• Topological Superconductors on Superstring Worldsheets
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• Conformal Perturbation Theory for Twisted Fields
• Moduli Anomalies and Local Terms in the Operator Product Expansion
• Conformal Contact Terms and Semi-Local Terms
• ADE Spectral Networks and Decoupling Limits of Surface Defects
• Notes on Superconformal Representations in Two Dimensions
• On exact correlation functions of chiral ring operators in $2d$ $\mathcal{N}=(2,2)$ SCFTs via localization
• On the Kähler-Hodge structure of superconformal manifolds
• Boundary Weyl anomaly of $\mathcal{N}=(2,2)$ superconformal models
• Revisiting the $k$-theorem with the ANEC