The large central charge limit of conformal blocks

TL;DR

This paper investigates conformal blocks in W3 symmetric conformal field theories at large central charge, deriving explicit forms, differential equations, and analyzing singularities, thus advancing understanding of their mathematical structure.

Contribution

It provides explicit calculations of conformal blocks in the large central charge limit, including differential equations and singularity analysis, for theories with W3 symmetry.

Findings

Conformal blocks expressed as sl3-invariant functions.

Agreement with combinatorial Young diagram expansion.

Identification of a sixth-order differential equation and a new singularity at z=-1.

Abstract

We study conformal blocks of conformal field theories with a W3 symmetry algebra in the limit where the central charge is large. In this limit, we compute the four-point block as a special case of an sl3-invariant function. In the case when two of the four fields are semi-degenerate, we check that our results agree with the block's combinatorial expansion as a sum over Young diagrams. We also show that such a block obeys a sixth-order differential equation, and that it has an unexpected singularity at z=-1, in addition to the expected singularities at z=0,1,infinity.