A 'novel' pure theory of Einstein-Gauss-Bonnet gravity in four-spacetime dimensions can be constructed by rescaling the Gauss-Bonnet coupling constant, seemingly eluding Lovelock's theorem. Recently, however, the well-posedness of this model has been called into question. Here we apply a 'dimensional regularization' technique, first used by Mann and Ross to write down a D → 2 limit of general relativity, to the case of pure Einstein-Gauss-Bonnet gravity. The resulting four-dimensional action is a particular Horndeski theory of gravity matching the result found via a Kaluza-Klein reduction over a flat internal space. Some cosmological solutions of this four-dimensional theory are examined. We further adapt the technique to higher curvature Lovelock theories of gravity, as well as a low-energy effective string action with an α correction. With respect to the D → 4 limit of the α -corrected string action, we find we must also rescale the dilaton to have a non-singular action in four dimensions. Interestingly, when the conformal rescaling Φ is interpreted as another dilaton, the regularized string action appears to be a special case of a covariant multi-Galileon theory of gravity.

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We revisit the cutoff surface formulation of fluid-gravity duality in the context of the classical double copy. The spacetimes in this fluid-gravity duality are algebraically special, with Petrov type II when the spacetime is four dimensional. We find two special classes of fluids whose dual spacetimes exhibit higher algebraic speciality: constant vorticity flows have type D gravity duals, while potential flows map to type N spacetimes. Using the Weyl version of the classical double copy, we construct associated single-copy gauge fields for both cases, finding that constant vorticity fluids map to a solenoid gauge field. Additionally we find the scalar in a potential flow fluid maps to the zeroth copy scalar.

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We show generalized Galileons — a particular subclass of Horndeski gravity — arise from a consistent Kaluza-Klein reduction of the low-energy effective action of heterotic string theory to first order in α'. This suggests Horndeski theories of gravity have a string-theoretic origin. The form of the Galileonic terms is precisely fixed by parameters of the embedding spacetime, so that only a specific subset of Horndeski theories is permitted by string theory. A novel limit of the model is considered by performing a dimensionfulrescaling of α'.