Superconformal Symmetry in the Kaluza-Klein Spectrum of Warped AdS(3)

TL;DR

This paper analyzes the Kaluza-Klein spectrum of warped AdS3 compactifications in type IIB string theory, revealing bounds on fluctuation spectra, superpartner structures, and connections to the dual SCFT's chiral ring, with explicit examples involving Y^{p,q} theories.

Contribution

It demonstrates the boundedness of fluctuation spectra, identifies superpartners, and links the mesonic chiral ring to Kohn-Rossi cohomology in warped AdS3 compactifications.

Findings

Spectra of spin 2 and axio-dilaton fluctuations are bounded.

Modes at the bound correspond to chiral primaries and their superpartners.

The mesonic chiral ring relates to first Kohn-Rossi cohomology groups.

Abstract

We study the Kaluza-Klein spectrum of warped $AdS_3$ compactifications of type IIB with five-form flux which are dual to $\mathcal{N}=(0,2)$ SCFTs in two dimensions. We prove that the spectra of fluctuations of both the spin 2 sector of the graviton and the axio-dilaton are bounded. At the bound the modes have the correct quantum numbers to be chiral primaries and descendants thereof respectively. Moreover, we prove that the same modes give rise to superpartners in the dilatino spectrum. Our results show that a subset of the mesonic chiral ring of the dual SCFT is isomorphic to the first Kohn-Rossi cohomology groups. As an example, we consider the compactification of four-dimensional $Y^{p,q}$ theories on Riemann surfaces for the case of the universal twist. We conclude by studying fluctuations of the three-form, where we are able to identify Betti multiplets after imposing some mild assumptions.