On Normal Modes of a Warped Throat

TL;DR

This paper analyzes the spectrum of scalar and pseudoscalar glueball modes in a warped deformed conifold, revealing their relation to supermultiplets and implications for flux compactifications.

Contribution

It provides a detailed calculation of glueball spectra including non-zero momentum and explores their supermultiplet structure in warped throat geometries.

Findings

Discrete spectrum of $0^{+-}$ glueballs derived

Spectrum of $0^{--}$ pseudoscalar glueballs obtained

Modes form massive supermultiplets

Abstract

As shown in arXiv:hep-th/0405282, the warped deformed conifold has two bosonic massless modes, a pseudoscalar and a scalar, that are dual to the phase and the modulus of the baryonic condensates in the cascading gauge theory. We reconsider the scalar mode sector, mixing fluctuations of the NS-NS 2-form and the metric, and include non-zero 4-d momentum $k_\mu$. The resulting pair of coupled equations produce a discrete spectrum of $m_4^2=- k_\mu^2$ which is interpreted as the spectrum of $J^{PC}= 0^{+-}$ glueballs in the gauge theory. Similarly, we derive the spectrum of certain pseudoscalar glueballs with $J^{PC}= 0^{--}$, which originate from the decoupled fluctuations of the RR 2-form. We argue that each of the massive scalar or pseudoscalar modes we find belongs to a 4-d massive axial vector or vector supermultiplet. We also discuss our results in the context of a finite length throat embedded into a type IIB flux compactification.