A new Ricci flat geometry

TL;DR

This paper introduces a novel Ricci-flat metric derived from an infinite family of Sasaki-Einstein geometries, extending Calabi-Yau spaces with a free parameter, and explores its supergravity solutions with D-branes.

Contribution

It constructs a new Ricci-flat geometry from $Y^{(p,q)}$ spaces with a parameter s, generalizing known Calabi-Yau solutions and analyzing associated supergravity backgrounds.

Findings

New Ricci-flat metric from $Y^{(p,q)}$ geometries with parameter s.

Supergravity solutions with D3 branes on the new geometry.

Logarithmic behavior of five-form flux with a different argument.

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.