61st North British Mathematical Physics Seminar

Abstract: A black hole spacetime has characteristic excitations called quasinormal modes. Using the AdS/CFT duality, the quasinormal modes of a AdS black hole correspond to the collective modes of the thermal state of a strongly interacting quantum field theory. While the complete spectrum of modes depends upon the details of the spacetime, in this talk I will explain that exact constraints on the spectrum can be obtained by studying just the dynamics near the event horizon. In the dual quantum field theories this is related to a phenomenon called pole-skipping, and leads to a universal relation between hydrodynamics and chaos in such theories.

Abstract: W. Bardeen has suggested a long time ago that the non-vanishing of the one-loop same helicity YM amplitudes, in particular such an amplitude at four points, should be interpreted as an anomaly. More recently, the non-vanishing of this amplitude in YM and gravity was shown to be linked to the UV divergence of the two-loop quantum gravity. In this talk, I will first describe a new computation of the same helicity box amplitude by a method designed to mimic the chiral anomaly derivation. I will then show that the box diagram is related to the sum of bubble diagrams which are shift dependent, owing to an identity which states that the sum of box, triangles and bubbles vanish with some particular choice of loop momenta. The bubble diagrams can be computed by insertion of currents to one or both of the legs of the bubbles. I will explain how this can possibly lead to interpret an anomaly of the currents in the self-dual sector of YM.

Abstract: I will describe modern amplitude techniques in the context of gravity and electrodynamics. In particular, I will focus on black hole physics and on ways to efficiently compute observables using double copy relations. I will then explain how analytic continuation to a split signature spacetime can help us understand some important features, such as classical radiation and full gravity solutions. This will also allow us to make an explicit connection between the classical and the quantum version of the double copy.

Abstract: Abstract: One of the main successes of string theory is the matching of the macroscopic and microscopic calculations of black-hole entropies. The macroscopic calculation requires a black-hole solution of the equations of motion of the effective theory and an entropy formula (like A/4 in Einstein's theory). Many solutions are known at leading order in alpha' and, at this order, the entropy formula is just A/4. Due to the terms of higher order in curvatures, finding the alpha' corrections to the leading-order black-hole solutions is a complicated problem which only recently has been solved for some of them in the context of the heterotic theory, but an entropy formula for them was still lacking and no reliable comparison between microscopic and macroscopic entropies was, actually, possible. In this talk I will present an entropy formula for heterotic black holes valid to first order in alpha'. The presence of terms of higher order in curvatures demands the use of Wald's formalism, but the presence of fields with gauge freedoms (specially the Kalb-Ramond 2-form, with its Nicolai-Townsend gauge transformations) forbids the naive use of the standard Iyer-Wald prescription, because it gives gauge-dependent results. We show how to treat those fields in the context of Wald's formalism using "momentum maps" to define transformations of all the fields under diffeomorphisms which vanish for Killing vectors in a gauge-invariant way ("gauge-covariant Lie derivatives"). We prove the first law of black-hole mechanics in this context making use of "restricted generalized zeroth laws". This proof identifies the expression that plays the role of entropy, which is gauge-invariant.