Physics / research
Conformal fields and consistency constraints
Develop conformal representations, correlation functions, operator products, and bootstrap reasoning with clear distinctions between exact results and numerical bounds.
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Inside this module
Module 01 research
Conformal fields and consistency constraints
Develop conformal representations, correlation functions, operator products, and bootstrap reasoning with clear distinctions between exact results and numerical bounds.
- 01
Conformal algebra and primary operators
Specify Euclidean conformal representations before interpreting dimensions, spin and descendants.
35 min - 02
Radial quantization and the state-operator map
Turn scale transformations into cylinder evolution with the correct adjoint and energy reference.
35 min - 03
Two- and three-point conformal correlators
Derive the coordinate dependence fixed by symmetry while keeping normalization and OPE data explicit.
35 min - 04
Operator product expansion and convergence
Use a separating sphere to understand when a conformal operator expansion converges.
35 min - 05
Conformal blocks and Casimir equations
Package descendants into blocks while fixing the channel, eigenvalue and small-distance branch.
35 min - 06
Crossing symmetry and reflection positivity
Combine alternative OPE channels with the precise positivity needed for bootstrap inequalities.
35 min - 07
Unitarity bounds and short representations
Derive dimension restrictions from descendant norms while stating the identity and representation exceptions.
35 min - 08
Two-dimensional Virasoro symmetry
Distinguish local holomorphic symmetry, central extension and Virasoro descendants from the global subalgebra.
35 min - 09
Minimal models and modular invariance
Combine null-state representation data with the separate consistency of left-right torus spectra.
35 min - 10
Numerical bootstrap bounds and truncation control
Read an exclusion as a conditional consistency result and separate it from constructing a conformal theory.
35 min