Stress-energy tensor deformations, Ricci flows and black holes

This paper reviews and extends the recently discovered connections between marginal and irrelevant stress-energy tensor deformations and gravity theories in arbitrary space-time dimensions. We start by discussing how TT̄ and Root-TT̄ deformations of two-dimensional field theories can be equivalently interpreted as the coupling of the undeformed matter sector to a gravity theory. We then extend this duality to higher-dimensional scenarios by using an approach that relies on the non-trivial eigenvalue degeneracy characterising the energy-momentum tensor of specific physical theories. We also explore incorporating dynamical degrees of freedom in the gravity sector, and show that the deformed space-time geometry induced by the TT̄-like deformations defines a Ricci-Bourguignon flow of the metric tensor, which reduces to a Ricci flow in four dimensions. Finally, exploiting a dressing-type mechanism for the action functional characterizing a broad class of TT̄-like deformations we study explicit examples, such as Einstein-Ricci solitons, $(d-1)$-form field theories, and spherically symmetric electrovacuum solutions.