Speaker
Description
The holographic duality provides a powerful framework for understanding strongly interacting conformal field theories, and more generally, quantum field theories. The AdS/CFT correspondence, its prime and most concrete example, is largely based on the connection between the isometry group of the AdS spacetime and the conformal group, but is not exhausted by this.
The main statement of the holographic duality says that a gravitational theory in a d-dimensional spacetime is completely equivalent to a non-gravitational quantum theory living on its (d-1)-dimensional boundary. Thus, we are able to extract information on QFT observables at strong coupling by performing calculations on the gravitational side of the duality.
However, neither the bulk gravity theory nor the dual field theory is free from pathological divergent behavior. To find correct relations for quantities, it is necessary to perform the holographic regularization and renormalization to remove divergences systematically and consistently. These procedures are similar to those in QFT. As in QFT, the renormalization procedure in holography leads to the notion of renormalization group flows proposed in the works of E. Akhmedov, K. Skenderis, J. de Boer, E. and G. Verlinde. From the holographic side, RG flows are described in terms of gravitational domain walls with AdS boundaries and certain boundary conditions for the bulk fields. In particular, thanks to the boundary conditions, the gravitational Hamiltonian equations can be reduced to the form of the Callan-Symanzik equation. The holographic RG flow is associated with the RG flow of the dual field theory between conformal fixed points, triggered either by a relevant operator or a non-zero VEV of an operator. The UV divergences of the dual field theory correspond to the IR divergences on the gravitational side.
A special case is represented by thermal RG flows, which allow us to study the consistency of dual CFTs and the dynamics of the near-horizon region of black holes. In the framework of holographic duality, the RG flows at finite temperature are described by asymptotic AdS black holes, and their behavior near the horizon encodes the thermalization process in the dual CFT.
In my talk I give a review of basic aspects and recent progress of holographic RG flows at zero and finite temperatures and present a way of studying them through the dynamical systems.
