Advanced Quantum Field Theory (Spring 2022)

Tue, Thur 11am @ Zoom (link will be shared in the ETL. 56-321 classroom is also reserved.)

Prof. Sunghoon JUNG

TA: 최재혁

All information in this page is also available in the ETL. They are collected in a single page here.

1. Renormalization
• Renormalization:   DIMREG, MS-bar. RG evolution:   beta function, anomalous dimension, dimensional transmutation. Green's function:   Callan-Symanzik, meanings, RG scale choice. Wilsonian RG:   new viewpoints.
• P&S   Ch.12 (7,10),   Schwartz   Ch.23, 21 (16, 18, 19),   Srednicki   Ch.27~29
• Further topics:   QCD asymptotic freedom,  Appelquist-Carazzone decoupling theorem,   gauge coupling unification,   QCD DGLAP evolution.
• J. Polchinski   "Renormalization and effective Lagrangian" NPB 231 (1984)
2. Spontaneous Symmetry Breaking   &   Criticality
• SSB:  Goldstone thm, Higgs mechanism, the role of the Higgs. Renormalizability:   linear sigma model, effective action (background field method). Criticality:   universality, Wilson-Fisher fixed points, epsilon expansion. General d:   non-linear sigma model, Wilsonian RG, large N.
• P&S   Ch.11, 13, (20.1),    Schwartz   Ch.28, 34,    Srednicki   Ch.21, 30~32
• Further topics:   background field method,   thermodyn variables in QFT,   quantization of spon broken gauge thy,   Banks-Zaks fixed point,   Stueckelburg U(1).
• B. Lee, C. Quigg, H. Thacker   "Weak interactions at very high energies: the role of the Higgs-boson mass" PRD 16 (1977)
3. Anomaly
• Chiral anomaly:   2d vacuum polarization, operator product, chiral flows, 4d triangle. Gauge anomaly:   chiral gauge current, SM, mixed anomaly. 't Hooft anomaly:   anomaly matching, QCD chiral sym breaking. Finally topological:   path integral measure, Atiyah-Singer index, instantons. Scale anomaly:   scale transform, trace anomaly in d=4.
• P&S Ch.19 (with supplement on "Instantons"),    D. Tong "Gauge Theory" Ch. 3,    J. Harvey "Anomalies" Ch.1, 2,   Srednicki Ch.93.
• Further topics:   gauge anomalies in MSSM,   strong CP and axion,   instanton profile,   IR nature,   SU(2) anomaly,   D_mu under delta g_munu,   instanton det operator
4. Effective Field Theory:   Simplicity against naturalness?
• Matching. Operator renormalization and mixing. Chiral Lagrangian. SM as an EFT.
• P&S Ch.18.1-2, 19.3,    Schwartz Ch.25.2, 22,    D. Tong "Gauge Theory" Ch.5,    H. Georgi "Effective Field Theory"
• Further topics:   CCWZ method,   mesons with Nf=3,  
5. Emergence:   Chern-Simons
• Topological effects:   in Chiral Lagrangian, Quantum Hall effect. Chern-Simons theory.   Emergent U(1).   Non-Abelian Chern-Simons.  
• R. Shankar QM Ch.21,   D. Tong "Quantum Hall Effect" Ch.2, 5,   E. Witten "Topological Phases of Matter" Ch.2, 3.
• Further topics:   topological insulator,   edge modes and anomaly,   bulk-boundary correspondence,   knots (ref below),   anyon braiding, ...
• E. Witten "QFT and the Jones Polynomial", D. Arovas et al "Fractional statistics and QHE".
6. Conformality:   Conformal Field Theory
• Conformal transformation. Quantum aspects. Central charge.
• Polchinski Ch.2 and 15,   D. Tong "String Theory" Ch.4, 1,   P&S 18.3,   The yellow book.
• Further topics:   Virasoro algebra,   entanglement entropy,   rational CFT,   c-theorem
7. Genesis:   Hawking and de Sitter
• QFT in curved spacetime. Unruh effect. BH. de Sitter temperature.
• Carroll Ch.9,   Mukhanov & Winitzki Ch.6~9.
• Further topics:   BH thermodynamics,   Conformal diagrams,   dS coordinates,   quantum effects in FRW,   BH information problem