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Abstract |
We use holographic renormalization of minimal N=2 gauged supergravity in order to derive the general form
of the quantum Ward identities for 3d N=2 and 4d N=1 superconformal theories on general curved
backgrounds, including an arbitrary fermionic source for the supercurrent. The Ward identities for 4d N=1
theories contain both bosonic and fermionic global anomalies, which we determine explicitly up to quadratic
order in the supercurrent source. The Ward identities we derive apply to any superconformal theory,
independently of whether it admits a holographic dual, except for the specific values of the a and c anomaly
coefficients, which are equal due to our starting point of a two-derivative bulk supergravity theory. We show
that the fermionic anomalies lead to an anomalous transformation of the supercurrent under rigid
supersymmetry on backgrounds admitting Killing spinors, even if all superconformal anomalies are
numerically zero on such backgrounds. The anomalous transformation of the supercurrent under rigid
supersymmetry leads to an obstruction to the Q-exactness of the stress tensor in supersymmetric vacua, and
may have implications for the applicability of localization techniques. We use this obstruction to the Q-
exactness of the stress tensor, together with the Ward identities, in order to determine the general form of
the stress tensor and R-current one-point functions in supersymmetric vacua, which allows us to obtain
general expressions for the supersymmetric Casimir charges and partition function. The talk is based on
arXiv:1703.04299. |
