On Normal Modes of a Warped Throat

TL;DR

The paper advances the holographic study of the Klebanov–Strassler throat by computing the spectra of normal modes odd under the I-symmetry: radial excitations of the GHK scalar from coupled NSNS B_2–metric fluctuations and a separate RR-sector pseudoscalar. It derives and analyzes coupled radial equations, computes their spectra numerically, and demonstrates how these modes organize into massive 4d supermultiplets (axial-vector and vector partners). It further explores how a finite throat and bulk compactification influence the masses, highlighting UV sensitivity for the baryonic-sector Higgs-like mode. Overall, the work extends prior 0^{++} analyses to new sectors, offering a detailed framework for glueball spectra in strongly coupled gauge theories with gravity duals and implications for string phenomenology in flux compactifications.

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 $k_μ$. The resulting pair of coupled equations produce a discrete spectrum of $m_4^2=- k_μ^2$ 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.

Figures (1)

• Figure 1: The dependence of $\log \tilde{m}$ on $\tau_{\max}$ is linear with the slope equal to -$1/3$. The three lines shown correspond to $\delta=1$, $\delta=0.01$ and $\delta=0.0001$.