Gravity Duals of Fractional Branes and Logarithmic RG Flow

TL;DR

This paper explores the gravity duals of fractional D3-branes in orbifold and conifold theories, revealing how these branes induce logarithmic RG flows and modify the dual supergravity backgrounds.

Contribution

It provides explicit supergravity solutions for fractional branes in orbifold and conifold setups, linking geometric perturbations to field theory beta-functions and RG flows.

Findings

Fractional branes correspond to localized twisted sector scalars.

Solutions are holomorphic functions matching field theory beta-functions.

Logarithmic RG flows are reproduced in the dual supergravity backgrounds.

Abstract

We study fractional branes in ${\CN}=2$ orbifold and ${\CN}=1$ conifold theories. Placing a large number $N$ of regular D3-branes at the singularity produces the dual ${\bf AdS}_5\times X^5$ geometry, and we describe the fractional branes as small perturbations to this background. For the orbifolds, $X^5={\bf S}^5/\Gamma$ and fractional D3-branes excite complex scalars from the twisted sector which are localized on the fixed circle of $X^5$. The resulting solutions are given by holomorphic functions and the field-theoretic beta-function is simply reproduced. For $N$ regular and $M$ fractional D3-branes at the conifold singularity we find a non-conformal ${\cal N}=1$ supersymmetric $SU(N+M)\times SU(N)$ gauge theory. The dual Type $\II$B background is ${\bf AdS}_5\times {\bf T}^{1,1}$ with NS-NS and R-R 2-form fields turned on. This dual description reproduces the logarithmic flow of couplings found in the field theory.