Gravity Dual of Superconformal Anomaly

Abstract

The supergravity dual of superconformal anomaly in a four-dimensional supersymmetric gauge theory is investigated. We consider a well-established dual correspondence between the $\mathcal{N}=1$ $SU(N+M)\times SU(N)$ supersymmetric gauge theory with two flavors of matter fields in the bifundamental representation of gauge group and the type IIB superstring in the space-time background furnished by the Klebanov-Strassler (K-S) solution. The D-brane configuration for these two dual theories consists of N D3 branes and M fractional $D3$ branes in the singular space-time composed of a direct product of M^4 and a six-dimensional conifold ${\mathcal{C}}_6$ with the base $T^{1,1}$. The superconformal anomaly originate from fractional branes frozen at the apex of ${\mathcal{C}}_6$. While on the gravity side, the fractional branes deform the $Ad{S}_5\times T^{1,1}$ space-time background and partially break local supersymmetry of type IIB supergravity. We find that the deformation on $Ad{S}_5\times T^{1,1}$ leads to the spontaneous breaking local symmetries in gauged AdS_5 supergravity and consequently a super-Higgs mechanism arises. We thus conclude that the super-Higgs mechanism in gauged supergravity is dual to the superconformal anomaly of supersymmetric gauge theory in terms of gauge/gravity correspondence.

49 pages, RevTex 4, no figures, shortened version