Effective Theory Interpretation of Deformations of Klebanov-Strassler Geometry

The accelerated expansion of the universe implies a small and positive cosmological constant, corresponding to a de Sitter (dS) vacuum. However, constructions of string theory vacua are typically Anti-de Sitter (AdS), corresponding to a negative cosmological constant. In the model proposed by Kachru, Kallosh, Linde, and Trivedi (KKLT), anti-D3 branes are added to a highly warped region of the Klebanov-Strassler (KS) background to produce a dS vacuum. The warping is crucial to ensure that the resulting positive cosmological constant is small due to gravitational redshift. However, the anti-D3 branes deform the background geometry and could destroy the compactification in the worst case. To understand the deformations, we calculate the possible fluctuations of the KS geometry, the Kaluza-Klein (KK) modes of the geometry. We find that the spectra of the KK modes are quantized and exhibit approximate quadratic growth, and the modes are localized in the infrared (IR). We will then compare these KK modes with the variations of the warp factor and the internal metric as functions of the conifold deformation parameter.