LisMath Seminar 

26/04/2021, 10:00 — 10:30 — Online
Pedro Aniceto, LisMath, Instituto Superior Técnico, Universidade de Lisboa

Integrability and holography in dimensionally reduced theories of gravity in 2 dimensions

This talk is divided into two parts. In the first part, we consider the Riemann-Hilbert factorization approach to the construction of Weyl metrics. We prove that the canonical Wiener-Hopf factorization of a matrix obtained from a general monodromy matrix, with respect to an appropriately chosen contour, yields a solution to the gravitational field equations. We show moreover that, by taking advantage of a certain degree of freedom in the choice of the contour, the same monodromy matrix generally yields distinct solutions to the field equations.

In the second part, we approach the problem of constructing the holographic dictionary for the AdS$_2$/CFT$_1$ correspondence for higher derivative gravitational actions in AdS$_2$ spacetimes obtained by an $S^2$ reduction of 4-dimensional $\mathcal{N}=2$ Wilsonian effective actions with Weyl squared interactions. We focus on BPS black hole solutions, for which we show how the Wald entropy of these black holes is holographically encoded in the dual CFT. Additionally, using a 2D/3D lift we show that the dual CFT$_1$ is naturally embedded in the chiral half of the CFT$_2$ dual to the AdS$_3$ spacetime.