PHY573 Quantum Field Theory III

This course covers the basic concepts of effective field theories (EFTs) and quantum field theories beyond the Standard Model (SM). We will start by introducing the core concept of constructing EFTs and apply them to the SM Lagrangian.

In the next part of the course, we will discuss Chiral Perturbation Theory (ChPT), the low-energy effective theory of Quantum Chromodynamics (QCD). After this, the concept is applied to describe a class of theories beyond the SM, in which the SM Higgs arises as a composite state of a new confining sector.

For the remainder of the course, we will focus our attention to the concept of Supersymmetry (SUSY), starting from the discussion of the SUSY algebra and its representations, to arrive, after the presentation of the superspace formalism, to the construction of the supersymmetric version of gauge field theories

Main topics:

• Introduction to Effective Field Theories
• Decoupling and matching
• Renormalization group resummation
• The Standard Model Effective Field Theory (SMEFT)
• Chiral Lagrangians
• Composite Higgs models
• The SUSY algebra
• Superspace and superfields
• Supersymmetric actions
• Minimal Supersymmetric Standard Model (MSSM)

Part I (EFT):

• A. Manohar, Effective field theories, Lect. Notes Phys. 479 (1997) 311.
• D. Kaplan, Five lectures on effective field theory 

Part II (Chiral Lagrangians)

• A. Pich, Effective Field Theory with Nambu–Goldstone Modes
• A. Pich, Chiral Perturbation Theory
• G. Colangelo and G. Isidori, An Introduction to ChPT  
• A. Manohar, Effective Field Theories
• I. Stewart, MIT web course on Effective Field Theory
• R. Contino, The Higgs as a Composite Nambu-Goldstone Boson

Part III (SUSY):

• M. Bertolini, Lectures on Supersymmetry
• S. Martin, A Supersymmetry Primer
• J. Wess and J. Bagger, "Supersymmetry and supergravity".
• Mueller-Kirsten & Wiedemann, "Introduction to supersymmetry".
• S. Weinberg, "The quantum theory of fields. Vol. 3: Supersymmetry".