Shortening Anomalies in Supersymmetric Theories

Understand

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.