A modular invariant bulk theory for the c=0 triplet model

TL;DR

This paper constructs a modular invariant bulk theory for the c=0 triplet model using boundary-to-bulk reconstruction, ensuring consistency with known boundary states and partition functions.

Contribution

It proposes a new bulk space construction for the logarithmic W(2,3)-triplet model at c=0 based on boundary theory insights.

Findings

Bulk partition function is modular invariant.

Boundary state analysis matches annulus partition functions.

Bulk space is a quotient of projective representations.

Abstract

A proposal for the bulk space of the logarithmic W(2,3)-triplet model at central charge zero is made. The construction is based on the idea that one may reconstruct the bulk theory of a rational conformal field theory from its boundary theory. The resulting bulk space is a quotient of the direct sum of projective representations, which is isomorphic, as a vector space, to the direct sum of tensor products of the irreducible representations with their projective covers. As a consistency check of our analysis we show that the partition function of the bulk theory is modular invariant, and that the boundary state analysis is compatible with the proposed annulus partition functions of this model.