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Speaker: Giulio Bonelli (SISSA, Trieste, Italy)

Title: Applied SUSY QFT & BHPT: one loop corrections to near extremal (dS-)Kerr thermodynamics

Abstract: The study of Black-Hole perturbation theory [BHPT] is a classical problem in General Relativity
and crucial to study gravitational waves. As the high order of symmetry of the BH gravitational
field implies separation of variables, BHPT reduces to the study of 2nd order linear ordinary
differential equations (ODE). These ODEs have particular rational potentials and are solved
exactly by classical Virasoro conformal blocks. The latter have an explicit expression because
of AGT duality (BPS sector in susy gauge theory ≡CFT2) and the classical limit of crossing
relations generate the explicit solution of the connection problem of the ODE. Applying the solution
back to BHPT one gets a powerful computational technique. Quantitative and qualitative (exact)
results in BHPT have been obtained so far, such as grey-body factors, Love numbers, quasi-normal
modes, BH scattering amplitudes, effective actions in BH backgrounds. In particular, combining
with a generalisation of the Gelfand-Yaglom formula for singular potentials one gets an exact
expression for the one loop (dS-)Kerr effective action. The latter is shown to undergo a precise
scaling with the temperature and proves a conjecture made by means of qualitative arguments
on one-loop corrections to the entropy.