The Gauge/Gravity Theory of Blown up Four Cycles

TL;DR

This paper constructs explicit supersymmetric supergravity solutions for D3-branes on Calabi-Yau cones with blown-up 4-cycles, linking geometric deformations to field theory moduli and analyzing physical implications like confinement.

Contribution

It provides a universal geometric deformation of supergravity backgrounds for D3-branes on Calabi-Yau cones, including explicit solutions for Z_2 orbifolds and toric cases, connecting geometry with field theory operators.

Findings

Deformation corresponds to blowing up a 4-cycle in Calabi-Yau.

Explicit gravity solutions with two deformation parameters for Z_2 orbifold.

Probe analyses show linear confinement and insights into IR behavior.

Abstract

We present an explicit supersymmetric deformation of supergravity backgrounds describing D3-branes on Calabi-Yau cones. From the geometrical point of view, it corresponds to blowing up a 4-cycle in the Calabi-Yau and can be done universally. In the field theory, we identify this deformation with motion on non-mesonic directions in the full moduli space of vacua. For the case of a Z_2 orbifold of the conifold, we discuss an explicit gravity solution with two deformation parameters: one corresponding to blowing up a 2-cycle and one corresponding to blowing up a 4-cycle. The generic case where the Calabi-Yau is toric is also discussed in detail. Quite generally, the order parameter of these 4-cycle deformations is a dimension six operator. We also consider probe strings which show linear confinement and probe D7 branes which help in understanding the behavior far in the infrared.