Gravitational Correspondence of Two Types of Superconformal Anomaly

TL;DR

This paper explores two distinct superconformal anomaly multiplets in four-dimensional supersymmetric gauge theories and their dual representations in classical supergravity within the gauge/gravity correspondence framework.

Contribution

It clarifies the different origins and dual gravitational effects of two types of superconformal anomalies in supersymmetric gauge theories.

Findings

Anomaly from gauge dynamics corresponds to spontaneous symmetry breaking in supergravity.

Anomaly from external supergravity topology appears as boundary effects in AdS_5.

Distinct gravitational duals reflect different anomaly origins.

Abstract

In a classical conformal invariant supersymmetric gauge theory, the chiral R-symmetry current, the supersymmetry current and the energy-momentum tensor constitute a supercurrent multiplet. There are two different superconformal anoamly multiplets in four-dimensional supersymmetric gauge theories, one originating from the supersymmetric gauge dynamics and the consequent nonvanishing \beta-function, and the other one coming from the coupling of the supercurrent multiplet to the external supergravity multiplet with non-trivial topology. We emphasize that in the gauge/gravity dual correspondence these two types of superconformal anomaly multiplets have distinct reflections in the classical supergravity: the anomaly multiplet due to the supersymmetry gauge dynamics is dual to the spontaneous symmetry breaking and the consequent super-Higgs effect in AdS_5 bulk supergravity, while the anomaly multiplet originating from the non-trivial topology of external conformal supergravity mutiplet is a boundary effects of the AdS_5 space.