A day for gravity

This is the live session included as part of the LonTI lecture on Gravity and black holes in AdS. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom.Gravity in asymptotic AdS spacetimes behaves in many ways quite differently to the usual asymptotically flat situation we are usually introduced to. It is very important in understanding the AdS-CFT correspondence, and many of these differences to the flat setting have important implications. In this lecture and the problem sheet I will introduce AdS spacetime, asymptotic AdS spacetimes and then focus on the physics of black holes in AdS. For the simplest static black holes we will explore their behaviour, the implications for AdS-CFT and introduce some basic calculational tools to study them.

The release of the youtube video for the London Theory institute seminar series available at https://youtu.be/jtfmWDrC370. Gravity in asymptotic AdS spacetimes behaves in many ways quite differently to the usual asymptotically flat situation we are usually introduced to. It is very important in understanding the AdS-CFT correspondence, and many of these differences to the flat setting have important implications. In this lecture and the problem sheet I will introduce AdS spacetime, asymptotic AdS spacetimes and then focus on the physics of black holes in AdS. For the simplest static black holes we will explore their behaviour, the implications for AdS-CFT and introduce some basic calculational tools to study them.

We consider the energy of a (2+1)-d relativistic QFT on a deformation of flat space in either the quantum or thermal vacuum state. Looking at both free scalars and fermions, with and without mass (and in the scalar case including a curvature coupling) we surprisingly find that any deformation of flat space is always energetically preferred to flat space itself. This is a UV finite effect, insensitive to any cut- off. We see the same behaviour for any (2+1)-holographic CFT which we compute via the gravity dual. We consider the physical application of this to membranes carrying relativistic degrees of freedom, the vacuum energy of which then induce a tendency for the membrane to crumple. An interesting case is monolayer graphene, which experimentally is observed to ripple, and on large scales can be understood as a membrane carrying free massless Dirac degrees of freedom.

I will review the link between 1+p dimensional maximally supersymmetric Yang-Mills and the black hole thermodynamics of Dp-branes via the gauge/string correspondence. The finite temperature behaviour of Dp-brane supergravity black holes looks very alien from the perspective of the dual strongly coupled Yang-Mills. However, I will argue that in a natural set of Yang-Mills variables, the classical moduli (which unfortunately are still strongly coupled), certain features of these thermodynamics become quite transparent.

Compact Calabi-Yau manifolds are a key ingredient for dimensional reduction in string theory. For this, one requires the Ricci-flat metric on these manifolds. Whilst Yau proved this metric exists, no explicit smooth examples are known, essentially as it is very difficult (impossible?) to find them analytically as they have no continuous isometries. Taking a new approach, I will discuss numerical methods to solve the Einstein equation on these manifolds. I will pedagogically describe the construction, and give results, for a particular one parameter family of metrics on K3 (the unique 4-dimensional Calabi-Yau manifold). I will discuss possible applications of these methods, and generalizations to geometries with matter such as those relevant for flux compactifications. There will be some nice pictures.