Renormalization Group Flows on D3 branes at an Orbifolded Conifold

TL;DR

This work analyzes RG flows for ${\cal N}=1$ quiver gauge theories realized on D3 branes at an orbifolded conifold by constructing and examining its gravity dual. It performs a two-step resolution of the orbifolded geometry to produce a smooth horizon $\widetilde{X_5}$ with a rich set of $2$-cycles, enabling fractional D3 branes to wrap D5 branes on these cycles in a brane-box setup. By turning on RR flux through the conifold-singularity cycles and NS-NS flux through the resolved $2$-cycles, the authors derive a logarithmic running of the gauge couplings, matching the field-theory beta functions via the AdS/CFT correspondence. This provides a concrete gravity dual of non-conformal RG flows in a chiral $\mathcal{N}=1$ quiver and clarifies the role of twisted moduli and fluxes in orbifolded horizons.

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.

Figures (8)

• Figure 1: An Interval Model
• Figure 2: A toric diagram for ${\bf Z}_2\times {\bf Z}_3$ hyper-quotient of the conifold, ${\cal C}_{23}$
• Figure 3: A toric diagram for $\widetilde{{\cal C}_{23}}$
• Figure 4: A Brane Box Model
• Figure 5: A toric diagram for $\widehat{{\cal C}_{23}}$