Advanced QFT and Supersymmetry

This collection covers non-Abelian gauge theory, effective field theory, supersymmetry, and generalized symmetries. Its scope includes Yang–Mills models, gauge fixing and BRST/BV methods, instantons and lattice regulators; Wilsonian actions, matching, running, operator redundancies, and amplitude positivity; supermultiplets, superspace, supersymmetric actions, vacuum structure, and symmetry breaking. Further branches address localization, protected indices, BPS solitons, wall crossing, spectral networks, topological defects, higher-form and non-invertible symmetries, and anomalies. Model-specific deductions, formal perturbative constructions, duality questions, and experimental constraints remain distinct, with their assumptions and approximation regimes stated explicitly.

Quantum Field Theory supplies field and observable conventions, while Quantum Field Theory Mathematics develops the gauge, graded-algebra, localization, and defect constructions required here. Lie Theory, Differential Geometry, Algebraic Topology, and Hall Algebras and Tensor Categories provide additional geometric and algebraic foundations. The collection is intended to support later String Theory, Supergravity, and Dualities, String Compactifications and Phenomenology, and Holography and Quantum Black Holes. Those downstream categories belong to the proposed string-theory programme; these connections describe intended uses rather than completed builds.