We study boundary conditions for 3-dimensional higher spin gravity that admit asymptotic symmetry algebras expected of 2-dimensional induced higher spin theories in the light cone gauge. For the higher spin theory based on sl(3, R) plus sl(3,R) algeb
ra, our boundary conditions give rise to one copy of classical W3 and a copy of sl(3,R) or su(1,2) Kac-Moody symmetry algebra. We propose that the higher spin theories with these boundary conditions describe appropriate chiral induced W-gravity theories on the boundary. We also consider boundary conditions of spin-3 higher spin gravity that admit u(1) plus u(1) current algebra.
We provide a set of chiral boundary conditions for three-dimensional gravity that allow for asymptotic symmetries identical to those of two-dimensional induced gravity in light-cone gauge considered by Polyakov. These are the most general boundary co
nditions consistent with the boundary terms introduced by Compere, Song and Strominger recently. We show that the asymptotic symmetry algebra of our boundary conditions is an sl(2,R) current algebra with level given by c/6. The fully non-linear solution in Fefferman--Graham coordinates is also provided along with its charges.
We consider counterterms for odd dimensional holographic CFTs. These counterterms are derived by demanding cut-off independence of the CFT partition function on $S^d$ and $S^1 times S^{d-1}$. The same choice of counterterms leads to a cut-off indepen
dent Schwarzschild black hole entropy. When treated as independent actions, these counterterm actions resemble critical theories of gravity, i.e., higher curvature gravity theories where the additional massive spin-2 modes become massless. Equivalently, in the context of AdS/CFT, these are theories where at least one of the central charges associated with the trace anomaly vanishes. Connections between these theories and logarithmic CFTs are discussed. For a specific choice of parameters, the theories arising from counterterms are non-dynamical and resemble a DBI generalization of gravity. For even dimensional CFTs, analogous counterterms cancel log-independent cut-off dependence.
We set up the BPS equations for a D3-brane moving in AdS_5 times S^5 which preserves two supercharges and with all bosonic fields turned on in the world-volume theory. By solving these, we find generalizations of Mikhailov giants and wobbling dual-gi
ants that include electromagnetic waves propagating on their world-volume. For these giants (dual-giants) we show that the BPS field strength is the real part of the pull-back of a holomorphic 2-form in the ambient space C^3 (C^{1,2}) onto the world-volume.
We derive the BPS equations for D3-branes embedded in AdS_5 X S^5 that preserve at least two supercharges. These are given in terms of conditions on the pullbacks of some space-time differential four-forms. Solutions to our equations are shown to des
cribe all the known giant and dual-giant gravitons in AdS_5 X S^5. We then argue that the configuration spaces of dual-giants can be mapped to non-compact hyperbol
