A new Ricci flat geometry

TL;DR

This work introduces a new six-dimensional Ricci-flat geometry that generalizes the Calabi–Yau cone over a Sasaki-Einstein family Y(p,q) by a modulus s. In the limit where s vanishes it reduces to the ordinary Calabi–Yau cone, and it admits a warped Type IIB supergravity solution with D3-branes and fluxes that preserves N=1 supersymmetry. A key finding is that the integrated five-form flux over the internal cycle exhibits logarithmic behavior with a novel argument, signaling interesting dual field theory dynamics. The modulus s acts as a closed-string modulus providing a tunable deformation of the internal geometry, extending holographic backgrounds based on irregular Sasaki-Einstein bases.

Abstract

We are proposing a new Ricci flat metric constructed from an infinite family of Sasaki-Einstein, $Y^{(p,q)}$, geometries. This geometry contains a free parameter $s$ and in the $s\to 0$ limit we get back the usual CY. When this geometry is probed both by a stack of D3 and fractional D3 branes then the corresponding supergravity solution is found which is a warped product of this new 6-dimensional geometry and the flat $R^{3,1}$. This solution in the specific limit as mentioned above reproduces the solution found in hep-th/0412193. The integrated five-form field strength over $S^2\times S^3$ goes logarithmically but the argument of Log function is different than has been found before.