Anabalon, A., Astefanesei, D., Choque, D., & Martinez, C. (2016). Trace anomaly and counterterms in designer gravity. J. High Energy Phys., (3), 29 pp.
Abstract: We construct concrete counterterms of the BalasubramanianKraus type for Einsteinscalar theories with designer gravity boundary conditions in AdS(4), so that the total action is fi nite onshell and satisfy a well de fi ned variational principle. We focus on scalar fi elds with the conformal mass m(2) = 2l(2) and show that the holographic mass matches the Hamiltonian mass for any boundary conditions. We compute the trace anomaly of the dual fi eld theory in the generic case, as well as when there exist logarithmic branches of nonlinear origin. As expected, the anomaly vanishes for the boundary conditions that are AdS invariant. When the anomaly does not vanish, the dual stress tensor describes a thermal gas with an equation of state related to the boundary conditions of the scalar fi eld. In the case of a vanishing anomaly, we recover the dual theory of a massless thermal gas. As an application of the formalism, we consider a general family of exact hairy black hole solutions that, for some particular values of the parameters in the moduli potential, contains solutions of fourdimensional gauged N = 8 supergravity and its omegadeformation. Using the AdS/CFT duality dictionary, they correspond to triple trace deformations of the dual fi eld theory.

Anabalon, A., Astefanesei, D., & Oliva, J. (2015). Hairy black hole stability in AdS, quantum mechanics on the halfline and holography. J. High Energy Phys., (10), 15 pp.
Abstract: We consider the linear stability of 4dimensional hairy black holes with mixed boundary conditions in Antide Sitter spacetinie. We focus on the mass of scalar fields around the maximally supersymmetric vacuum of the gauged N = 8 supergravity in four dimensions, m(2) = 2l(2). It is shown that the Schrodinger operator on the halfline, governing the S2, H2 or R2 invariant mode around the hairy black hole, allows for nontrivial selfadjoint extensions and each of them corresponds to a class of mixed boundary conditions in the gravitational theory. Discarding the selfadjoint extensions with a negative mode impose a restriction on these boundary conditions. The restriction is given in terms of an integral of the potential in the Schrodinger operator resembling the estimate of Simon for Schrodinger operators on the real line. In the context of AdS/CFT duality, our result has a natural interpretation in terms of the field theory dual effective potential.

Anabalon, A., Deruelle, N., & Julie, F. L. (2016). EinsteinKatz action,variational principle, Noether charges and the thermodynamics of AdSblack holes. J. High Energy Phys., (8), 15 pp.
Abstract: In this paper we describe 4dimensional gravity coupled to scalar and Maxwell fields by the EinsteinKatz action, that is, the covariant version of the “GammaGamma – GammaGamma” part of the Hilbert action supplemented by the divergence of a generalized “Katz vector”. We consider static solutions of Einstein's equations, parametrized by some integration constants, which describe an ensemble of asymptotically AdS black holes. Instead of the usual Dirichlet boundary conditions, which aim at singling out a specific solution within the ensemble, we impose that the variation of the action vanishes on shell for the broadest possible class of solutions. We will see that, when a longrange scalar “hair” is present, only subfamilies of the solutions can obey that criterion. The KatzBicakLyndenBell (“KBL”) superpotential built on this (generalized) vector will then give straightforwardly the Noether charges associated with the spacetime symmetries (that is, in the static case, the mass). Computing the action on shell, we will see next that the solutions which obey the imposed variational principle, and with Noether charges given by the KBL superpotential, satisfy the Gibbs relation, the Katz vectors playing the role of “counterterms”. Finally, we show on the specific example of dyonic black holes that the subclass selected by our variational principle satisfies the first law of thermodynamics when their mass is de fined by the KBL superpotential.

Chandia, O., Linch, W. D., & Vallilo, B. C. (2017). Master symmetry in the AdS(5) x S5 pure spinor string. J. High Energy Phys., (1), 15 pp.
Abstract: We lift the set of classical nonlocal symmetries recently studied by Klose, Loebbert, and Winkler in the context of Z(2) cosecs to the pure spinor description of the superstring in the AdS(5) x S5 background.

Chandia, O., Mikhailov, A., & Vallilo, B. C. (2013). A construction of integrated vertex operator in the pure spinor sigmamodel in AdS(5) x S5. J. High Energy Phys., 2013(11), 11 pp.
Abstract: Vertex operators in string theory me in two varieties: integrated and unintegrated. Understanding both types is important for the calculation of the string theory amplitudes. The relation between them is a descent procedure typically involving the bghost. In the pure spinor formalism vertex operators can be identified as cohomology classes of an infinitedimensional Lie superalgebra formed by covariant derivatives. We show that in this language the construction of the integrated vertex from an unintegrated vertex is very straightforward, and amounts to the evaluation of the cocycle on the generalized Lax currents.
