NUTs and bolts beyond Lovelock

Abstract

We construct a plethora of new Euclidean AdS-Taub-NUT and bolt solutions of several fourand six-dimensional higher-curvature theories of gravity with various base spaces B. In D = 4, we consider Einsteinian cubic gravity, for which we construct solutions with B = S 2 , T 2 . These represent the first generalizations of the Einstein gravity Taub-NUT/bolt solutions for any highercurvature theory in four dimensions. In D = 6, we show that no new solutions are allowed for any Generalized quasi-topological gravity at cubic order. They exist however when we consider quartic Quasi-topological and Generalized quasi-topological terms, for which we construct new solutions with B = CP 2 , S 2 × S 2 , S 2 × T 2 , T 2 × T 2 . In all cases, the solutions are characterized by a single metric function, and they reduce to the corresponding ones in Einstein gravity when the higher-curvature couplings are set to zero. While the explicit profiles must be constructed numerically (except for a few cases), we obtain fully analytic expressions for the thermodynamic properties of all solutions. The new solutions present important differences with respect to Einstein gravity, including regular bolts for arbitrary values of the NUT charge, critical points, and re-entrant phase transitions.

Partition functions on slightly squashed spheres and flux parameters

“…Until recently, no additional AdS-Taub-NUT solutions were known in d+1 = 4 bulk dimensions for any other metric theories of gravity. However, new solutions of that kind have been recently constructed in [60] for cubic and quartic higher-order gravities of the so-called Generalized Quasi-topological (GQT) class [61][62][63][64][65][66][67][68][69][70][71][72][73][74]. Remarkably, the thermodynamic properties of such solutions can be obtained fully analytically -and nonperturbatively in the higher-order couplings-in all cases.…”

“…in general dimensions and at arbitrarily high orders in curvature [70], and they have many interesting properties, such as possessing second-order equations of motion when linearized around maximally symmetric backgrounds, or the fact that the thermodynamic properties of their black hole solutions can be computed analytically -see e.g., [69] for a detailed summary. For the purposes of this work, the most relevant aspect is that a certain subset of GQT theories admit solutions of the AdS-Taub-NUT class which are also characterized by a single function and whose thermodynamic properties can be computed analytically [60,81,82]. As explained in [12,60], the relevant solutions take the general form 20) where n is the NUT charge (not to be confused with the order of the higher-curvature terms).…”

“…For the purposes of this work, the most relevant aspect is that a certain subset of GQT theories admit solutions of the AdS-Taub-NUT class which are also characterized by a single function and whose thermodynamic properties can be computed analytically [60,81,82]. As explained in [12,60], the relevant solutions take the general form 20) where n is the NUT charge (not to be confused with the order of the higher-curvature terms). For even (d + 1), one can replace CP Similarly to ψ in Eq.…”

“…The standard way of performing such calculation involves the introduction of generalized versions [84,85] of the Gibbons-Hawking boundary term [86,87] as well as counterterms [32,33,56,57] which render the resulting action finite. A simplified method which only requires the Einstein gravity boundary term plus knowledge of F S d -or, equivalently, the quantity customarily denoted a * -valid for GQTs was introduced in [53] and successfully applied later in [60,88].…”

“…Let us start our study of five-dimensional CFTs by analyzing the quartic theories for which explicit AdS-Taub-NUT solutions were constructed in [60]. The free energy of those solutions was also computed in the same paper, and it was later observed [12] that the resulting expressions match the general formula (2.21).…”