Report：AdS/CFT and Hamiltonian formalism of gravity

Speaker：Dr. WU Jieqiang （UCSB）

Chair：Prof. LING Yi（IHEP）

Time：10 am, Tuesday, Jan. 25, 2022

Zoom：4456457666 / 123456 (code)

Link：https://ihep-ac-cn.zoom.us/j/4456457666?pwd

Abstract:

The Hamiltonian formalism of gravity is very important, for example in studying black hole interior, initial value problem, and microscopic states counting. When constructing the Hamiltonian formalism, one needs to take use of the diffeomorphism symmetries to simplify the formalism. In this talk, I will introduce two of my works in this direction: covariant phase space formalism and diffeomorphism invariant observables.

In the first work, I construct the covariant phase space formalism for systems with spatial boundaries. The covariant phase space formalism is a covariant Hamiltonian formalism, which is widely used in gravity. However, this formalism suffers several ambiguities related to the boundary terms. In this work, we give a new version of the formalism, which incorporates the boundary effects from the very beginning. Our formalism resolves all of the previous ambiguities, and leads to a systematical algorithm for constructing the phase space and Hamiltonian.

In the second work, I study the diffeomorphism invariant observables and their brackets in a simple model: Jackiw-Teitelboim gravity coupled with matter fields. With the brackets, we can easily reproduce some recent results in Jackiw-Teitelboim gravity: traversable wormhole, an SL(2) algrabra, butterfly effect. We also study the excitation energy for an excitation deep in the gravity, with which we try to clarify the black hole firewall paradox.

Reference: arXiv: 1906.08616, 2108.04841