Index for Supergravity on AdS_5 \times T^{1,1} and Conifold Gauge Theory

TL;DR

This paper computes the superconformal index for the conifold gauge theory using its AdS/CFT dual, type IIB supergravity on $AdS5 x T^{1,1}$. By extracting the BPS spectrum with $\Delta = 0$ from the KK reduction and exponentiating the single-particle index, the author obtains a closed form for the index: $\mathcal{I}^W_{con}(t,y) = \prod_{n=1}^\infty \frac{(1-y^{-n}t^{3n})(1-y^n t^{3n})}{(1-t^{3n})^4}$. The gauge theory interpretation identifies gravity states with single-trace BPS operators, including a baryon-current multiplet (Betti multiplet) and exactly marginal deformations from harmonic forms on $T^{1,1}$, with IR-free $U(1)$ decoupled to fit the AdS/CFT dictionary. The work demonstrates a protected BPS sector that remains invariant under marginal deformations and motivates extensions to other Sasaki–Einstein spaces and finite-$N$ corrections.

Abstract

We compute the index for the conifold gauge theory from type IIB supergravity (superstring) on AdS_5 \times T^{1,1}. We discuss its implication from the gauge theory viewpoint.