2D Conformal Bootstrap

Virasoro Algebra · Minimal Models · Crossing Symmetry · Operator Spectrum

Minimal Model Selection

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Operator Spectrum Table

Crossing Symmetry

Fusion Rules

Select a model to see fusion rules.

Theory

Minimal model M(p,q): c = 1 − 6(p−q)²/pq
Kac table: h_{r,s} = ((pr−qs)²−(p−q)²)/4pq
Bootstrap: 4-pt function <φφφφ> satisfies
crossing symmetry F(z)=F(1−z) (Zamolodchikov)
Conformal block G_{Δ,ℓ}(z,z̄) encodes exchange
Virasoro algebra: [L_m, L_n] = (m−n)L_{m+n} + c/12·m(m²−1)δ_{m+n,0}
Primary: L_n|h⟩=0 for n>0, L_0|h⟩=h|h⟩