A Gravity Dual of the Chiral Anomaly

TL;DR

The paper studies how a chiral $U(1)$ R-symmetry anomaly in a cascading $SU(N+M)\times SU(N)$ gauge theory is realized holographically. It shows the anomaly is encoded in the UV supergravity solution as a non-invariance of the RR two-form $C_2$ under $U(1)$ rotations of the angle $\beta$, yielding the field-theory anomaly equation $\partial_i J^i = \frac{M}{16\pi^2}(F^a_{ij}\tilde F^{aij} - G^b_{ij}\tilde G^{bij})$ and reducing the symmetry to ${\bf Z}_{2M}$, with IR breaking to ${\bf Z}_2$. In AdS$_5$, the anomaly manifests as spontaneous symmetry breaking: the bulk vector dual to the R-current acquires mass by absorbing a scalar dual to the difference of $\Theta$ angles, a bulk Higgs mechanism that also yields an anomalous dimension for the current, $\Delta-3 \approx (g_s M)^2/[\pi (g_s N)]$. The ${\cal N}=2$ ${\bf Z}_2$ orbifold is analyzed and shown to reproduce the same anomaly coefficients, with gravity matching field-theory expectations even when flavors are added via D7-branes. Together, these results illustrate how quantum anomalies in gauge theories map to classical bulk dynamics in holography and extend to orbifold and flavor-generalized settings.

Abstract

We study effects associated with the chiral anomaly for a cascading $SU(N+M)\times SU(N)$ gauge theory using gauge/gravity duality. In the gravity dual the anomaly is a classical feature of the supergravity solution, and the breaking of the U(1) R-symmetry down to ${\bf Z}_{2M}$ proceeds via the Higgs mechanism.