The unitary subsector of generalized minimal models

Abstract

We revisit the line of non-unitary theories that interpolate between the Virasoro minimal models. Numerical bootstrap applications have brought about interest in the four-point function involving the scalar primary of lowest dimension. Using recent progress in harmonic analysis on the conformal group, we prove the conjecture that global conformal blocks in this correlator appear with positive coefficients. We also compute many such coefficients in the simplest mixed correlator system. Finally, we comment on the status of using global conformal blocks to isolate the truly unitary points on this line.

28+14 pages, 10 figures, PDF LaTeX, v2: Added footnote, v3: Published version, v4: Fixed factor of 2 and its side effects

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• Positivity, low twist dominance and CSDR for CFTs
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• Analytic Studies of Fermions in the Conformal Bootstrap
• Fusion of spin fields in $W_3$ conformal field theories
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• Conformal Bootstrap with Duality-Inspired Fusion Rule