Correlations of primary fields in the critical Ising model

Understand

We prove convergence of renormalized correlations of primary fields, i.

• e., spins, disorders, fermions and energy densities, in the scaling limit of the critical Ising model in arbitrary finitely connected domains, with fixed (plus or minus) or free boundary conditions, or mixture thereof.
• We describe the limits of correlations in terms of solutions of Riemann boundary value problems, and prove their conformal covariance.
• Moreover, we prove fusion rules, or operator product expansions, which describe asymptotics of the scaling limits of the correlations as some of the points collide together.