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Advanced Course for graduate students:

Scattering Amplitudes in Gauge/String Duality

Time:    Apr 13 (9:30-12:00am), Apr 17 (2:30-5:00pm), Apr 20 (9:30-12:00am),

              Apr 24 (2:30-5:00pm), Apr 27 (9:30-12:00am),

              May 04 (9:30-12:00am), May 08 (2:30-5:00pm)

 

Venue:  ITP Old Building 322

 

Lecture 1: Background, Motivation, and Introduction to Amplitudes

A general overview

Double line graph and Large Nc expansion

Color factor, color graph, color decomposition

Spinor helicity formalism, Little group, 3-pt amplitudes

Feynman diagram and MHV amplitudes

Lecture 2: Aspects of Unitarity for Amplitudes

S-matrix unitarity

Dispersion relation

Transcendental functions and branch cuts

On-shell unitarity cuts

4-cut and 2-cut for the 4-point 1-loop amplitude

Lecture 3: Conformal Symmetry and Wilson Loops

Conformal algebra and representations

Dual conformal symmetry of loop amplitudes

Introduction to Wilson loops

Feynman diagram computation of Wilson loops

Conformal Ward identity and BDS ansatz

Lecture 4: AdS/CFT Correspondence and Classical Strings

Eikonal limit and non-Abelian exponentiation

Introduction to AdS/CFT correspondence

Aspects of AdS geometry and coordinates

Introduction to classical string theory

Lecture 5: Introduction to the Alday-Maldacena pictures

Three simple minimal surface problems and solutions:

Quark-anti-quark potential, circular WL, single cusp WL

The picture of Gross-Mende

The picture of Alday-Maldacena

Lecture 6: T-duality and Four-Cusp Solution

Introduction to T-duality

T-duality for amplitudes in AdS

Four-cusp solution

Regularization and the area 

Lecture 7: Integrability

Yangian symmetry in 4D and in 2D

Why Sine-Gordon equation is integrable

Pohlmeyer reduction for AdS string

Hitchin equation and spectral parameter

Y-system and area

Open remarks

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