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The aim of this paper is to elucidate a close connection between the black hole area law and the infinite distance conjecture in the context of the swampland. We consider families of black hole geometries, parametrized by their event horizon areas or by the values of their entropies, and show that the infinite entropy limit is always at infinite distance in the space of black hole geometries. It then follows from the infinite distance conjecture that there must be a tower of states in the infinite entropy limit, and that ignoring these towers on the horizon of the black hole would invalidate the effective theory when the entropy becomes large. We call this the black hole entropy distance conjecture. We then study two candidates for the tower of states. The first are the Kaluza-Klein modes of the internal geometry of extremal ${cal N}=2$ black holes in string theory, whose masses on the horizon are fixed by the ${cal N}=2$ attractor formalism, and given in terms of the black hole charges similarly to the entropy. However, we observe that it is possible to decouple their masses from the entropy, so that they cannot generically play the role of the tower. We thus consider a second kind of states: inspired by N-portrait quantum models of non-extremal black holes, we argue that the Goldstone-like modes that interpolate among the black hole microstates behave like the expected light tower of states.
It has been conjectured that in theories consistent with quantum gravity infinite distances in field space coincide with an infinite tower of states becoming massless exponentially fast in the proper field distance. The complex-structure moduli space
We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropies
The volume of a black hole under noncommutative spacetime background is found to be infinite, in contradiction with the surface area of a black hole, or its Bekenstein-Hawking (BH) entropy, which is well-known to be finite. Our result rules out the p
Superconformal five dimensional theories have a rich structure of phases and brane webs play a crucial role in studying their properties. This paper is devoted to the study of a three parameter family of SQCD theories, given by the number of colors $
We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory having an i