Higher-derivative holography with a chemical potential

Abstract

We carry out an extensive study of the holographic aspects of any-dimensional higher-derivative Einstein-Maxwell theories in a fully analytic and non-perturbative fashion. We achieve this by introducing the d-dimensional version of Electromagnetic Quasitopological gravities: higher-derivative theories of gravity and electromagnetism that propagate no additional degrees of freedom and that allow one to study charged black hole solutions analytically. These theories contain non-minimal couplings, that in the holographic context give rise to a modified 〈JJ〉 correlator as well as to a general 〈TJJ〉 structure whose coefficients we compute. We constrain the couplings of the theory by imposing CFT unitarity and positivity of energy (which we show to be equivalent to causality in the bulk) as well as positive-entropy bounds from the weak gravity conjecture. The thermodynamic properties of the dual plasma at finite chemical potential are studied in detail, and we find that exotic zeroth-order phase transitions may appear, but that many of them are ruled out by the physical constraints. We further compute the shear viscosity to entropy density ratio, and we show that it can be taken to zero while respecting all the constraints, providing that the chemical potential is large enough. We also obtain the charged Rényi entropies and we observe that the chemical potential always increases the amount of entanglement and that the usual properties of Rényi entropies are preserved if the physical constraints are met. Finally, we compute the scaling dimension and magnetic response of twist operators and we provide a holographic derivation of the universal relations between the expansion of these quantities and the coefficients of 〈JJ〉 and 〈TJJ〉.

Corrections to AdS5 black hole thermodynamics from higher-derivative supergravity

“…The boundary terms associated with a generic higher-derivative bulk action such as (3.15) are not known, although several effective prescriptions have been discussed in the literature before, see e.g. [33,53,54] and references therein. In our simpler effective action (3.7), the only four-derivative invariant for which the associated Gibbons-Hawking term…”

Cosmological higher-curvature gravities

“…First, one could investigate the addition of (nonminimally coupled) matter to Cosmological Gravities, such as a scalar field or a U(1) gauge field. Regarding this last point, it is known that the definition of GQTGs may be canonically extended to allow for non-minimal couplings to a U(1) vector [41,[118][119][120][121], so it makes sense to explore whether a similar situation may occur for Cosmological Gravities, Also, the inclusion of this type of matter has mainly been considered in the context of minimally coupled nonlinear electrodynamics [122][123][124], so this aspect deserves careful scrutiny. Second, a natural question would be the addition of terms with covariant derivatives of the curvature, expected to appear from an effective field theory perspective.…”

Quasi-topological gravities on general spherically symmetric metric

“…It can be shown that quasi-topological gravity satisfies this condition and thus is a subclass of GQTG. Features of GQTG have been studied comprehensively at present [18][19][20][21][22][23][24][25][26][27]. In particular, (1.2) implies [26] the equation of f (r) is at most second order, the existence of Schwarzschild-like solutions, and most importantly, the decoupling of the extra massive modes.…”