Gravity duals of quantum distances

This paper provides a holographic approach to compute some most-frequently used quantum distances and quasi-distances in strongly coupling systems and conformal field theories. By choosing modular ground state as the reference state, it finds that the trace distance, Fubini-Study distance, Bures distance and Rényi relative entropy, all have gravity duals. Their gravity duals have two equivalent descriptions: one is given by the integration of the area of a cosmic brane, the other one is given by the Euclidian on-shell action of dual theory and the area of the cosmic brane. It then applies these duals into the 2-dimensional conformal field theory as examples and finds the results match with the computations of field theory exactly.

Non-Kähler deformed conifold, ultraviolet completion and supersymmetric constraints in the baryonic branch

Gravity duals for a class of UV complete minimally supersymmetric nonconformal gauge theories require deformed conifolds with fluxes. However these manifolds do not allow for the standard Kähler or conformally Kähler metrics on them, instead the metrics are fully non-Kähler. We take a generic such configuration of a non-Kähler deformed conifold with fluxes and ask what constraints do supersymmetry impose in the baryonic branch. We study the supersymmetry conditions and show that for the correct choices of the vielbeins and the complex structure all the equations may be consistently solved. The constraints now lead not only to the known cases in the literature but also to some new backgrounds. We also show how geometric features of these backgrounds, including the overall warp-factor and the resolution parameters, can be seen on the field theory side from perturbative “probe-brane” type calculations by Higgsing the theory and studying one-loop 4-point functions of vector and chiral multiplets. Finally we discuss how UV completions of these gauge theories may be seen from our setup, both from type IIB as well as from the T-dual type IIA brane constructions.