Rutgers University Department of Physics and Astronomy
Clay Mathematical Institute Lectures by Prof G.Moore
Lectures on Branes, K-theory and RR Charges
Overview
Outline of a Course I
Outline of a Course II
Outline of a course III
Lecture I: K-theory and Sewing Conditions
Motivation
Topological Field Theories
2D Case
Coherence of Sewing
The Cylinder Axiom
Frobenius Condition
The Closed String Sewing Theorem
Computing the Amplitudes I
Computing the Amplitudes II
Generalizing the Target
Frobenius Algebra Examples
Frobenius Algebra Example III
Frobenius Algebra Example IV: LG Models
Frobenius Algebra Example V: Cosmology
Closed and Open TFT
Closed and Open: Categories
Axioms for the Open Sector I
Axioms for the Open Sector II
Open/Closed Transition
Open and Closed Relations I
Open and Closed Relations II
The Double-Twist Diagram
The "Cardy Condition"
The Open and Closed Sewing Theorem
Semisimple Frobenius Algebras
Examples
Emergence of the "Spacetime" from an Algebra: Gelfand's Theorem I
Gelfand's Theorem II
Example
Emergence of Vector Bundles I
Emergence of Vector Bundles II
Emergence of Vector Bundles III
Emergence of Vector Bundles IV
Mixed Boundary Conditions
Mixed Boundary Conditions: Interpretation via Categories
Mixed Boundary Conditions: Conclusion
K-theory
The Boundary State
Remarks on (Semisimple) Boundary States
Boundary States as Hole Adding Operators
Extension to Families: vect -> K
Example
Baby Model of String Field Theory
Grothendieck Group
Fin.Gen. Projective Modules
K-theory from Projectors
Serre-Swan Theorem I
Serre-Swan Theorem II
Serre-Swan Theorem III
Morita Equivalence
Morita Equivalence:Examples
Summary
Speculation on Open Strings vs. Closed Strings
Please send any comments on this page to
G.Moore