제 2회 이론 물리 여름 학교

제 2 주 : Solitons and Instantons, Anomaly

강의 정보(tentative)

1. Anomaly


Lecture 1 : Global Anomaly a la Fujikawa
1) Global Anomaly at One Loop
2) Fujikawa
3) Basics of Heat Kernel
4) Axial Anomaly and Dirac Index (Density)
Exercise : Applications of Heat Kernel to Other One-Loop Computations
(Compute Beta Functions of Gauge Theories Coupled To Matter Fields)
Homework1-1
Homework1-2

Lecture 2 : Index & SUSY Quantum Mechanics
1) Quantum Mechanics : Heat Kernel vs. Path Integral
2) Index Densities via SUSY Quantum Mechanics Path Integral
Exercise :Fun with Quantum Mechanics Path Integrals
(fix various subtle items like normalzation of path integral of measures)

Lecture 3 : Local Anomaly
1) Local Anomaly and Wess-Zumino Consistency Condition
2) Local Anomaly from Index Densities
3) Anomaly Polynomials
Exercise : Understand Notations like p_n (Pontryagin density)
Evaluate Consistenty Anomaly Starting from Given Anomaly Polynomials

Lecture 4 & 5 : More on Local Anomaly
1) Examples of Gravitational Anomaly
2) Anomaly of Various Supersymmetric Theories in D=4,6,10
3) Gauge Anomaly in Odd Dimensions: Orbifold Field Theories
4) Anomaly at Classical Level
Exercise : To be announced

References:
1. Current Algebra and Anomaly
(Sam B. Treiman et al: Princeton University Press)
2. Please try to read as much as possible
Chaper 19 of "An Introduction to Quantum Field Theory"
by Peskin and Schroeder(Addison-Wesley)



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