We discuss holography for Schrodinger solutions of both topologically massive gravity in three dimensions and massive vector theories in (d+1) dimensions. In both cases the dual field theory can be viewed as a d-dimensional conformal field theory (tw
o dimensional in the case of TMG) deformed by certain operators that respect the Schrodinger symmetry. These operators are irrelevant from the viewpoint of the relativistic conformal group but they are exactly marginal with respect to the non-relativistic conformal group. The spectrum of linear fluctuations around the background solutions corresponds to operators that are labeled by their scaling dimension and the lightcone momentum k_v. We set up the holographic dictionary and compute 2-point functions of these operators both holographically and in field theory using conformal perturbation theory and find agreement. The counterterms needed for holographic renormalization are non-local in the v lightcone direction.
We set up precision holography for the non-conformal branes preserving 16 supersymmetries. The near-horizon limit of all such p-brane solutions with p leq 4, including the case of fundamental string solutions, is conformal to AdS_{p+2} x S^{8-p} with
a linear dilaton. We develop holographic renormalization for all these cases. In particular, we obtain the most general asymptotic solutions with appropriate Dirichlet boundary conditions, find the corresponding counterterms and compute the holographic 1-point functions, all in complete generality and at the full non-linear level. The result for the stress energy tensor properly defines the notion of mass for backgrounds with such asymptotics. The analysis is done both in the original formulation of the method and also using a radial Hamiltonian analysis. The latter formulation exhibits most clearly the existence of an underlying generalized conformal structure. In the cases of Dp-branes, the corresponding dual boundary theory, the maximally supersymmetric Yang-Mills theory SYM_{p+1}, indeed exhibits the generalized conformal structure found at strong coupling. We compute the holographic 2-point functions of the stress energy tensor and gluon operator and show they satisfy the expected Ward identities and the constraints of generalized conformal structure. The holographic results are also manifestly compatible with the M-theory uplift, with the asymptotic solutions, counterterms, one and two point functions etc of the IIA F1 and D4 appropriately descending from those of M2 and M5 branes, respectively. We present a few applications including the computation of condensates in Wittens model of holographic YM_4 theory.
We construct general 2-charge D1-D5 horizon-free non-singular solutions of IIB supergravity on T^4 and K3 describing fuzzballs with excitations in the internal manifold; these excitations are characterized by arbitrary curves. The solutions are obtai
ned via dualities from F1-P solutions of heterotic and type IIB on T^4 for the K3 and T^4 cases, respectively. We compute the holographic data encoded in these solutions, and show that the internal excitations are captured by vevs of chiral primaries associated with the middle cohomology of T^4 or K3. We argue that each geometry is dual to a specific superposition of R ground states determined in terms of the Fourier coefficients of the curves defining the supergravity solution. We compute vevs of chiral primaries associated with the middle cohomology and show that they indeed acquire vevs in the superpositions corresponding to fuzzballs with internal excitations, in accordance with the holographic results. We also address the question of whether the fuzzball program can be implemented consistently within supergravity.
