We analyse the dynamics of near-extremal Reissner-Nordström black holes in asymptotically four-dimensional Anti de Sitter space (AdS 4 ). We work in the spherically symmetric approximation and study the thermodynamics and the response to a probe scalar field. We find that the behaviour of the system, at low energies and to leading order in our approximations, is well described by the Jackiw-Teitelboim (JT) model of gravity. In fact, this behaviour can be understood from symmetry considerations and arises due to the breaking of time reparametrisation invariance. The JT model has been analysed in considerable detail recently and related to the behaviour of the SYK model. Our results indicate that features in these models which arise from symmetry considerations alone are more general and present quite universally in near-extremal black holes.

Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to the scalar four point function, in a particular limit. The derivation assumes approximate conformal invariance, and the conditions for the slow roll approximation, but is otherwise model independent. The Ward identities allow us to deduce that the three point function must be suppressed in general, being of the same order of magnitude as in the slow roll model. They also fix the three point function in terms of the four point function, upto one constant which we argue is generically suppressed. Our approach is based on analyzing the wave function of the universe, and the Ward identities arise by imposing the requirements of spatial and time reparametrization invariance on it.

Abstract:We derive the general Ward identities for scale and special conformal transformations in theories of single field inflation. Our analysis is model independent and based on symmetry considerations alone. The identities we obtain are valid to all orders in the slow roll expansion. For special conformal transformations, the Ward identities include a term which is non-linear in the fields that arises due to a compensating spatial reparametrization. Some observational consequences are also discussed.

Uncharged relativistic fluids in 3+1 dimensions have three independent thermodynamic transport coefficients at second order in the derivative expansion. Fluids with a single global U (1) current have nine, out of which seven are parity preserving. We derive the Kubo formulas for all nine thermodynamic transport coefficients in terms of equilibrium correlation functions of the energy-momentum tensor and the current. All parity-preserving coefficients can be expressed in terms of two-point functions in flat space without external sources, while the parity-violating coefficients require three-point functions. We use the Kubo formulas to compute the thermodynamic coefficients in several examples of free field theories. expansion, though their thermodynamic nature was not fully appreciated at the time. For fluids in 2+1 dimensions, analogous thermodynamic transport coefficients already appear at first order in the derivative expansion [5]. They have been variously referred to in the literature as "thermodynamic response parameters", "thermodynamic transport coefficients", "thermodynamical hydrodynamic coefficients", "equilibrium hydrodynamic coefficients", or "non-dissipative transport coefficients". 1 There is a multitude of notations for these coefficients in the literature, and the translation between different conventions is not always straightforward.While the thermodynamic transport coefficients were first noticed in the context of hydrodynamics [3][4][5], their connection with thermodynamics was not explored until [6,7]. These papers showed that the relevant coefficients in the constitutive relations follow from the equilibrium partition function, including the highly non-trivial constraints [5,8] demanded by the local positivity of entropy production. We will refer to the thermodynamic coefficients that appear in the constitutive relations as "thermodynamic transport coefficients", and to the coefficients in the equilibrium free energy as "thermodynamic susceptibilities". Thermodynamic transport coefficients are linear combinations of thermodynamic susceptibilities and their derivatives [6,7]. In the classification of non-dissipative transport coefficients in [9], thermodynamic transport coefficients correspond to class H S . 2 We will be considering fluids with a conserved global U (1) charge, such as the baryon number. We will refer to the fluids that can be locally described as having a temperature and a chemical potential for the global U (1) charge as "charged fluids". The system can be coupled to the corresponding non-dynamical external U (1) gauge field, and to the nondynamical external metric. The thermodynamic susceptibilities then include the usual "electric" and "magnetic" susceptibilities, as well as the response of the free energy to the vorticity, to the Riemann curvature, the magneto-vortical response, etc. In 3+1 dimensions, there are nine such susceptibilities at two-derivative order [6]. These susceptibilities will appear in the constitutive relations and in equilibrium correlation functions ...