Gravity Duals of Fractional Branes and Logarithmic RG Flow

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 ${\mathbf{AdS}}_5\times X^5$ geometry, and we describe the fractional branes as small perturbations to this background. For the orbifolds, $X^5={\mathbf{S}}^5/\Gamma$ 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 $\mathcal{N}=1$ supersymmetric $SU(N+M)\times SU(N)$ gauge theory. The dual Type $\II$B background is ${\mathbf{AdS}}_5\times {\mathbf{T}}^{1,1}$ 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.

15 pages, harvmac; v2: typos corrected; v3: minor corrections, references added

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