Strongly coupled theories and their use

The course illustrates the basic technical tools needed to deal with strongly-coupled relativistic quantum field theories, with applications to the QCD theory and to phyiscs beyond the Standard Model. In particular, the scenario of a composite Higgs boson is described.

Syllabus

• Exact unbroken symmetries: exact, approximate, broken and unbroken symmetries; the Noether theorem in QFT, conserved charges and commutators; selection rules; current matrix elements in an SO(2) example; application to charged pion 3-body decay.

• Spontaneously broken symmetries: a Z2 example: odd processes and selection rules, spontaneous versus explicit breaking; an SO(2) example: degenerate multiplets, massless Goldstones, non-linear symmetries and non-linear basis, the Golstone boson decay constant; non-Abelian symmetries and the Goldstone theorem; SO(n)/S(n-1) in the non-linear basis: Maurer-Cartan form and d/e symbols.

• The Symmetries of QCD: QCD Lagrangian; running coupling and confinement; discrete symmetries and baryon number; the flavor group; approximate Isospin and Gell-Mann symmetries; the symmetries in the hadron spectrum; an issue with light mesons; the chiral group; need for spontaneous breaking; the Gell-Mann-Levy sigma model; axial current and pion decay constant.

• The non-linear sigma model: the Goldstone matrix and its transformation properties; the two-derivatives Lagrangian; kinetic term and Goldstone interactions; the method of external sources; coupling to the photon and quark mass breaking; the meson spectrum.

• On Effective Field Theories, and NDA relativistic low-momentum effective field theories; a two-scalars example; effective theory and symmetries; the concept of matching; derivative expansion; classifying operators and field redefinitions; complete tree-level matching in the scalar example; the sigma-model as a low-energy effective field theory; matching with QCD and NDA formula; the maximal cutoff; applications to the Fermi theory and to quantum gravity.

• Composite Higgs, principles and applications the SM as an effective field theory; accidental symmetry, neutrino masses and proton decay; the Hierarchy Problem; dimensional transmutation; Goldstone bosons Higgs; minimal coset SO(5)/SO(4); the sigma-model of the composite Higgs; modified coupling to the SM gauge fields; SM fermions and Partial Compositeness; quarks in the fiveplet and Higgs-quarks coupling modification; a theory of flavor; anarchic partial compositeness.

Lecture Notes

• Exact Symmetries
• Broken Symmetries
• QCD and the Chiral Lagrangian
• Effective Field Theory
• Basics of Large-Nc
• Composite Higgs

Exam

Last modified: July 2013 - (andrea.wulzer@unipd.it)

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