We study local mirror symmetry on non-compact Calabi-Yau manifolds (conifold type of singularities) in the presence of D3 brane probes. Using an intermediate brane setup of NS 5-branes 'probed' by D4 resp. D5 branes, we can explicitly T-dualize three isometry directions to relate a non-compact Calabi-Yau manifold to its local mirror. The intermediate brane setup is the one that is best suited to read off the gauge theory on the probe. Both intervals and boxes of NS 5-branes appear as brane setups. Going from one to the other is equivalent to performing a conifold transition in the dual geometry. One result of our investigation is that the brane box rules as they have been discussed so far should be generalized. Our new rules do not need diagonal fields localized at the intersection. The old rules reappear on baryonic branches of the theory. * 1 The discussion of D3 branes on 6-dimensional singularities is very closely related to the by now famous AdS/CFT correspondence. Superconformal N = 2 or N = 1 (and also N = 0) gauge theories can be constructed as the duals of supergravity on AdS 5 ×X 5 , where X 5 is a certain five-dimensional (Einstein) manifold. First, for the case of D3 branes on six-dimensional orbifold singularities O = R 6 /Γ, where Γ is a discrete group, X 5 is given by S 5 /Γ, as discussed in [7,8]. The corresponding orbifold gauge theory can be calculated using string perturbation theory. The conifold singularities were later obtained in [6], where for the simplest conifold the corresponding Einstein space X 5 is the homogeneous space T 1,1 = (SU (2) × SU (2))/U (1). Further conifold type of singularities were recently discussed in [9].

In this note we construct a new class of superconformal field theories as mass deformed N = 4 super Yang-Mills theories. We will argue that these theories correspond to the fixed points which were recently found [1] studying the deformations of the dual IIB string theory on AdS 5 × S 5 . * 1 karch@ctp.mit.edu * 2 luest@physik.hu-berlin.de * 3 miemiec@physik.hu-berlin.de * 4 Allowing for orientifolds, the SO and Sp examples are also accessible.

This short note contains a detailed analysis to find the right power law the lowest eigenvalue of a localized massive graviton bound state in a four dimensional AdS background has to satisfy. In contrast to a linear dependence of the cosmological constant we find a quadratic one.

This is a review article of eleven dimensional supergravity in which we present all necessary calculations, namely the Noether procedure, the equations of motion (without neglecting the fermions), the Killing spinor equation, as well as some simple and less simple supersymmetric solutions to this theory. All calculations are printed in much detail and with explicit comments as to how they were done. Also contained is a simple approach to Clifford algebras to prepare the grounds for the harder calculations in spin space and Fierz identities.

We consider holographic RG flows which interpolate between non-trivial ultraviolet (UV) and infra-red (IR) conformal fixed points. We study the "superpotentials" which characterize different flows and discuss their expansions near the fixed points. Then we focus on the holographic c-function as defined from the two-point function of the stress-energy tensor. We point out that the equation for the metric fluctuations in the background flow is equivalent to a scattering problem and we use this to obtain an expression for the c-function in terms of the associated Jost functions. We propose two explicit models that realize UV-IR flows. In the first example we consider a thin wall separating two AdS spaces with different radii, while in the second one the UV region is replaced with an asymptotically AdS space. We find that the holographic c-function obeys the expected properties. In particular it reduces to the correct -nonzero -central charge in the IR limit. To obtain the expected large distance behavior of the central function it is necessary to subtract the contribution of a term quadratic in momentum. We argue that this corresponds to a state which does not belong to the conformal field theory. Instead it should be interpreted as due to the presence of dynamical gravity in the boundary theory.