Supersymmetry: Lecture Log

This is the lecture log for the Supersymmetry class PHY 396 T as taught in Fall 2025 by Professor Vadim Kaplunovsky.

Most lectures should be video recorded and the records available on Canvas. For the few lectures that did not get recorded because of technical glitches, I shall scan the notes I have used in class and links the scans to this page.

August 26 (Tuesday):

Syllabus and admin: textbooks and notes; prerequisite knowledge; class focus; lectures, homeworks, exams, and logistics.
Why supersymmetry: hierarchy and naturalness; GUTs, etc., exact non-perturbative results; use in string theory.
Conventions (quick overview).
Supersymmetric Higgs mechanism: each massive vector multiplet eats a whole scalar multiplet; SQED example in components and in superfields; moduli spaces beyond the Goldstone theorem.

August 28 (Thursday):

Intro to SQCD: the NA vector superfield; the NA gauge symmetry; the NA tension superfields W_α and W̅_α̇; complex gauge coupling and SQCD Lagrangian.
Higgs regime for the 1–flavor SQCD: VEVs, modulus, and eaten quark superfields; SUSY unitary gauge; vector masses in the superfield formulation.
SQCD with several flavors: sequential Higgs mechanism; moduli matrix M; rank(M) and the unbroken gauge group; moduli space geometry. Introduction to the Supersymmetric non-renormalization theorem: no perturbative corrections to the superpotential; consequences for the beta-functions.

September 2 (Tuesday):

Holomorphy: no counterterms except for δ^Z; consequences for beta-functions; holomorphy and chiral superfields; holomorphy and non-renormalization of the superpotential.
Effective classical action as generating functional of 1PI Feynman graphs (briefly).
Superfield Feynman rules for the Wess–Zumono model: superfield propagators and vertices; simple 1-loop example; delta-functions and their derivatives; 4-point example diagram; reading the operators graphically; higher derivatives of delta-functions.
non-renormalization theorem from superfield Feynman rules: evaluating the superspace integrals for a single loop; multi-loop diagrams; general form of superfield amplitudes; local versus nonlocal operators; no loop corrections to the superpotential. Started Infrared troubles: Infrared divergences leading to apparent δW.

September 4 (Thursday):

Infrared troubles: Infrared divergences leading to apparent δW; two-loop example; Wilsonian RG avoids the IR troubles.
Brief overview of the Wilsonian RG (cf. Peskin abd Schroeder, §12.1).
Holomorphy of the gauge couplings: Moduli dependent gauge couplings; holomorphic τ(M); harmonic 1/α and Θ; Wilsonian renormalization stops at 1 loop; conventional RG has higher-loop terms in beta-functions due to IR effects; Wilsonian coupling must be for the cutoff preserving SUSY and 4D gauge invariance; trouble with the dimensional reduction cutoff.
Begin SQED superfield Feynman rules: Massive propagators of chiral SF.

Extra lecture on September 5 (Friday):

Extended SUSY in 4D: Overview of extended supersymmetries in 4D: SUSY algebras; rigid N=2 and N=4 theories; supergravities with N=1,2,4,8; exotic theories with N=3,6.
Rigid N=2 multiplets: short and long multiplets; massless and short hypermultiplets; massless and short vector multiplets; long vector multiplets; Higgs mechanism and supermultiplets.
Non-abelian N=2 gauge theories: fields and the Lagrangian; allowed and forbiden quantum corrections.

September 11 (Tuesday):

Corrected superspace Feynman rules for the WZ model; rule for chiral SF propagators: arrow heads come with D̅² operators, arrow tails come with D² operators.
SQED Feynman rules: gauge fixing for the photon propagator; superfield Landau gauge; superfield Feynman gauge; ghosts; electron propagators and vertices; simple diagram examples.
SQED one-loop beta-function: the diagrams; evaluating the superspace integrals; the net momentum integral; the δ₃ counterterm, the anomalous dimension, and the beta-function; comparing to the component-field beta; generalizing to other theories.
Introduction to Ward–Takahashi identities of SQED: quick overview of WT identities in the ordinary QED; WT identities and renormalizability of SQED.

Tentative plan for September 13 (Thursday):

Ward–Takahashi identities for SQED: current superfield J; WT identities for purely photonic amplitudes; gauge symmetry and derivatives of external V superfields; no vector counterterms besides δ₂; WT identities for amplitudes with 2 electron lines; WT identities for the 1PI vertices and propagator dressings; the Ward identities for SQED.
Konishi anomaly for the axial current.

Tentative plan for September 18 (Tuesday):

Adler–Bardeen theorem and the θ angle: dressing up the anomaly at higher loops; axionic couplings of moduli scalars; moduli-dependent redefinition of the fermionic fields; canceling the anomaly by changing the θ angle.
Coupling SQED to moduli; modili-vector-vector amplitudes; redefinition of the charged superfields and the Konishi anomaly; canceling the anomaly by adjusting the Wilsonian gaguge coupling.
Relation between the Wilsonian and the physical gauge couplings; NSVZ (Novikov+Shifman+Vainshtein+Zakharov) formula; NSVZ beta function to all loop orders.