Dimension of sphere four-point bootstrap solution spaces with abelian monodromies

Determine whether the space of crossing-symmetry solutions for sphere four-point correlators with abelian monodromies has dimension floor r_1^2+r_2^2+r_3^2+r_4^2-/2 when the channel phases satisfy theta_s theta_t theta_u=theta_1 theta_2 theta_3 theta_4, independently of the allowed nontrivial phases.

Background

The paper studies deformations of critical loop models in which primary fields can have noninteger conformal spins while all fields in a given channel share a common phase. The resulting sphere four-point correlators have abelian monodromies, and the phase constraint theta_s theta_t theta_u=theta_1 theta_2 theta_3 theta_4 is required by monodromy consistency.

The conjecture asserts that allowing nontrivial phases does not change the finite dimension of the crossing-symmetry solution space from the dimension known or numerically supported in the single-valued critical loop models. The paper reports numerical evidence for the claim and reports finding no solutions when the phase constraint is violated.