A new covariant c-function is defined from extrinsic curvature of codimension-two bulk slices, unifying prior foliation-based definitions and exhibiting expected monotonic behavior in conformal, confining, and mixed-geometry string backgrounds.
3-branes on resolved conifold
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abstract
The type IIB supergravity solution describing a collection of regular and fractional D3 branes on the conifold (hep-th/0002159) was recently generalized to the case of the deformed conifold (hep-th/0007191). Here we present another generalization -- when the conifold is replaced by the resolved conifold. This solution can be found in two different ways: (i) by first explicitly constructing the Ricci-flat Kahler metric on resolved conifold and then solving the supergravity equations for the D3-brane ansatz with constant dilaton and (self-dual) 3-form fluxes; (ii) by generalizing the ``conifold'' ansatz of hep-th/0002159 in a natural ``asymmetric'' way so that the 1-d action describing radial evolution still admits a superpotential and then solving the resulting 1-st order system. The superpotentials for the ``resolved'' and ``deformed'' conifold cases turn out to have essentially the same simple structure. The solution in the resolved conifold case has the same asymptotic UV behaviour as in the conifold case, but unlike the deformed conifold case is still singular in the IR. The naked singularity is of repulson type and may have a brane resolution.
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Covariant unification of holographic c-functions
A new covariant c-function is defined from extrinsic curvature of codimension-two bulk slices, unifying prior foliation-based definitions and exhibiting expected monotonic behavior in conformal, confining, and mixed-geometry string backgrounds.