A family of solvable non-rational conformal field theories

TL;DR

This paper introduces a new family of exactly solvable non-rational conformal field theories in two dimensions, extending known models like Liouville and H3+ with a parameterized family of theories.

Contribution

It identifies and characterizes a family of solvable non-rational CFTs with explicit correlator relations to Liouville theory, including special cases like Liouville and H3+ models.

Findings

Correlators relate to Liouville theory correlators.

Special cases include Liouville and H3+ models.

Third-order differential equations govern correlators at m=2.

Abstract

We find non-rational conformal field theories in two dimensions, which are solvable due to their correlators being related to correlators of Liouville theory. Their symmetry algebra consists of the dimension-two stress-energy tensor, and two dimension-one fields. The theories come in a family with two parameters: the central charge c and a complex number m. The special case m=0 corresponds to Liouville theory (plus two free bosons), and m=1 corresponds to the H3+ model. In the case m=2 we show that the correlators obey third-order differential equations, which are associated to a subsingular vector of the symmetry algebra.