On normal modes of a warped throat

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.