In this lecture, Prof. Liu discusses how to calculate the entanglement entropy of a boundary system using the AdS gravity. He gives a holographic proof of the strong Sub-additivity conditions of the entanglement entropy, and discusses a simple example.

In this lecture, Prof. Liu continues discussion of Euclidean correlation functions by outlining the prescription for higher-point functions, then discusses evaluation of a Wilson loop of a boundary theory using the corresponding AdS string theory.

In this lecture, Prof. Liu first introduces general setup of string theory, including various forms of the string action and symmetries of the action. He then solves classical string dynamics in the light-cone gauge.

In this lecture, Prof. Liu introduces D-branes and finds spectrum (excitations) of open strings on D-branes. Among the excitations are massless vector fields whose low energy effective actions are given by a U(1) gauge theory.

In this lecture, Prof. Liu finishes the discussion of the computation of the Wilson loop, calculates the Coulomb potential between a heavy quark and anti-quark in N=4 SYM theory,and generalizes the duality to a finite temperature boundry system.

In this lecture, Prof. Liu covers the Hawking-page transition (the prediction that large N finite temperature boundary systems exhibit a first order phase transition at high temperature) and the duality in finite chemical potential boundary systems.

In this lecture, Prof. Liu continues discussion of physics of D-branes, including an overview of different types of D-branes in type II super string theory, and then description of D-branes as in terms of spacetime geometries.

In this lecture, Prof. Liu further explains two sides of the AdS / CFT duality, including a brief overview of string theory and gravity in AdS spacetime.

In this lecture, Prof. Liu goes deeper into the matching of spectrum of the two sides of the duality, how the mass of a field in AdS spacetime is related to the scaling dimension of the corresponding operator in the boundary theory.

This lecture begins Part 3 of the course: Duality Toolbox. In this lecture, Prof. Liu discusses general aspects of the duality, including the IR / UV connection and matching of symmetries, parameters and spectrum between two sides of the duality.

In this lecture, Prof. Liu first finishes discussing class string dynamics in the light-cone gauge, and then proceeds to quantize the theory in the light-cone gauge.

In this lecture, Prof. Liu motivates a prescription for obtaining Euclidean correlation functions of the boundary theory from bulk gravity, then discusses in detail the example of the computation of two-point functions.

In this lecture, Prof. Liu continues discussion of physics of D-branes, including low energy effective action, tension of D-branes, low energy effective theory of multiple coincidental D-branes, which are described by a non-Abelian gauge theory.

In this lecture, Prof. Liu continues discussion of theories whose fields are built out of matrices. When the rank N of the matrices become large, observables can be expanded in 1/N.

In this lecture, Prof. Liu discusses near-horizon geometry of a D3-brane and consider a limit which decouples the asymptotically flat region of the geometry. The same limit applied to low energy theory of D-branes then gives the AdS / CFT duality.

In this lecture, Prof. Liu gives a physical interpretation of the black hole temperature, and similarly the temperature experienced by an accelerated observer in Minkowski spacetime.

In this lecture, Prof. Liu discusses the concept of emergent gravity, and proves the Weinberg-Witten no go theorem which forbids existence of massless spin-2 particles. The beginning of the lecture is devoted to course information.

In this lecture, Prof. Liu first discusses closed string spectrum obtained from light-cone quantization. He then briefly discusses string interactions which confirms the interpretation of the graviton.

In the first part of this lecture, Prof. Liu explains physical motivation behind the holographic principle, and a formulation of the principle. In the second part, he starts a new topic on the large N limit of a non-Abelian gauge theory.

In this lecture, Prof. Liu connects the topological expansion of a matrix field theory in 1 / N to the perturbative expansion of a string theory. The structure of perturbative expansion of a string theory is explained from first principle.

In this lecture, Prof. Liu wraps up the mathematical connection between 1/N expansion of a large N matrix field theory with the perturbative expansion of a string theory. The second half of this lecture is an introduction to string theory.

In this lecture, Prof. Liu first discusses the causal structure of a black hole geometry, and that of a closely related spacetime called Rindler spacetime. He also derives a closely related phenomenon: Minkowski spacetime.

In this lecture, Prof. Liu first discusses important scales in classical and quantum gravity, and then reviews the spacetime geometry of a black hole.

In this lecture, Prof. Liu first discusses four laws of black hole mechanics, and then relate them to laws of thermodynamics. He also outlines black hole information paradox.