Modular invariance Z(tau+1) = Z(tau); period-1 e^{2 pi i} = 1

Layer 1 — Physicsin the conformal-field-theory subtree

Modular-invariance framework for CFT partition function on torus (Cardy 1986 Nucl Phys B 270, 186). Setup: 2D CFT on torus T^2 = C/(Z + tau Z) has partition function Z(tau) = Tr_H q^{L_0 - c/24} q-bar^{L_0-bar - c/24} with q = e^{2 pi i…

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