Renormalization Group Flows on D3 branes at an Orbifolded Conifold

TL;DR

This paper investigates the geometric resolution of orbifolded conifold singularities and explores the duality between string theory on the resolved space and the corresponding ${ m N}=1$ field theory, analyzing fluxes and RG flows.

Contribution

It provides a detailed geometric resolution of the orbifolded conifold and links flux configurations to field theory RG flows within the AdS/CFT framework.

Findings

Resolved the singular horizon into a smooth Einstein manifold.

Reproduced the logarithmic RG flow of couplings via flux analysis.

Demonstrated the duality between string backgrounds and ${ m N}=1$ field theories.

Abstract

We consider D3-branes at an orbifolded conifold whose horizon ${X_5}$ resolves into a smooth Einstein manifold which joins several copies of ${\bf T}^{1,1}$. We describe in details the resolution of the singular horizon ${X_5}$ and describe different types of two-cycles appearing in the resolution. For a large number of D3 branes, the AdS/CFT conjecture becomes a duality between type IIB string theory on $AdS_5 \times {X_5} $ and the ${\cal N} = 1$ field theory living on the D3 branes. We study the fractional branes as small perturbations of the string background and we reproduce the logarithmic flow of field theory couplings by studying fluxes of NS-NS and R-R two forms through different 2-cycles of the resolved horizon.