We find a class of new supersymmetric Euclidean solutions in four-dimensional maximal gauged supergravity. The holographic dual description of these backgrounds is given by a massdeformation of the ABJM theory with general values for the R-charges. We calculate the S 3 free energy for the supergravity backgrounds and find agreement with the supersymmetric localization calculation of the free energy in the large N limit.

We explore a fruitful connection between the physics of conformal field theories (CFTs) in ddimensional Minkowski spacetime and the extended gravitational thermodynamics of hyperbolic black holes in (d + 1)-dimensional anti-de Sitter spacetime. The CFTs are reduced on a region bounded by a sphere. We show that Renormalization Group flows between CFTs are specific thermodynamic processes in the (p, V ) plane, where the irreversibility of coarse-graining flows from the ultraviolet to the infrared corresponds to the Second Law of thermodynamics, preventing heat from flowing from low temperature to high. We observe that holographic heat engines using the black holes as a working substance correspond to specific combinations of CFT flows and deformations. We construct three special engines whose net heat and work can be described in terms of changes of entanglement entropy across the sphere. Engine efficiencies emerge as simple functions of the ratio of the number of degrees of freedom of two CFTs. arXiv:1806.05170v3 [hep-th] 17 Dec 2018 1 See e.g. ref. [8] for analogous expressions in other kinds of gravity theory. 2 See e.g. refs. [18-25], and ref. [26] for a survey of the literature with some applications. 3 Here we are neglecting properties such as charge and rotation, which would contribute with standard extra terms.

Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

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