Emergent gravity/Non-linear U(1) gauge theory correspondence

Kaluza-Klein gravity is revisted, with renewed interest, in a type IIB string theory on $S^1\times K3$. The irreducible curvature tensors are worked out in the, T-dual, emergent gravity in 4D to yield a non-linear U(1) gauge theory. Interestingly, the T-duality may be seen to describe an open/closed string duality at a self-dual string coupling. The obtained deformation in $AdS_5$ black hole is analyzed to introduce the notion of temperature in the emergent gravity underlying the recent idea of entropic force.