### Curricular Unit

Advanced Physics Topics 1

### Module

Introduction to Gauge/Gravity Duality (IGGD)

### Type

Tutorial: Reading and Study assignment

### Contact hours

18

### Professor/Researcher in charge

Miguel Costa and João Penedones , U. Porto

### Summary of Contents

The course in based on a set of online lectures of Perimeter institute, which will be attended by the students and professors in charge, complemented by discussions and problem sessions. The topics are:

Lecture 1
- Large-N Gage Theories and Matrix Models

Lecture 2 - Applications
of Matrix Models: 2D Quantum Gravity, Ising Models on Random
Surfaces, the Vandermonde Determinant & the Method of Orthogonal
Polynomials

Lecture 3 - Introduction to Holographic Duality:
Weinberg-Witten Theorem, RG Flow and Universality, The Holographic
Principle

Lecture 4 - The AdS/CFT Correspondence: Motivation,
Preliminary Dictionary, Matching of Degrees of Freedom

Lecture 5 -
Extending the Holographic Dictionary; AdS/CFT and the Decoupling
Argument

Lecture 6 - AdS/CFT: Matching Symmetries; Perturbing the
Correspondence; Scalar Fields on AdS Spacetimes

Lecture 7 -
Solving the Scalar Wave Equation on AdS: Scaling on the Boundary;
Real-time Issues

Lecture 8 - What can we learn from bulk
solutions? Deformation and Response; Linear Response Theory

Lecture
9 - Holography at Finite Temperature: Black Holes

Lecture 10 -
Holography at Finite Density; How to use Holography Responsibly;
Non-Fermi Liquids

Lecture 11 - Saddle-point Approximation to
Matrix Models; Path Integrals, World-line Formalism and Wilson
Loops

Lecture 12 - Path Ordered Exponentials; Wilson Lines; Wilson
Loops and the Potential Between Static Point-like Charges

Lecture
13 - The Haar Measure; Lattice Gauge Theory and Wilson Loops at
Strong Coupling; RG Analysis of the QCD 'String' Tension at Weak
Coupling

Lecture 14 - Holographic Wilson Loops; N=4
Super-Yang-Mills via Dimensional Reduction; Supersymmetric
Wilson Loops

Lecture 15 - Supersymmetric Wilson Loops, Catalan Numbers and Matrix Models

### Evaluation

Problems solved and presented by the students during the course.