The puzzle of bulk conformal field theories at central charge c=0

TL;DR

This paper investigates bulk logarithmic conformal field theories at central charge c=0, revealing that the parameter b differs from boundary values and exploring the implications for correlation functions and theory relations.

Contribution

The study provides the first lattice-based measurement of the logarithmic partner parameter b in bulk LCFTs at c=0, showing it differs from boundary values and offering a theoretical explanation.

Findings

b = -5 for bulk theories, not the expected boundary values

The chiral stress tensor has a single logarithmic partner

Bulk-boundary relations in LCFTs are more complex than in non-logarithmic cases

Abstract

Non-trivial critical models in 2D with central charge c=0 are described by Logarithmic Conformal Field Theories (LCFTs), and exhibit in particular mixing of the stress-energy tensor with a "logarithmic" partner under a conformal transformation. This mixing is quantified by a parameter (usually denoted b), introduced in [V. Gurarie, Nucl. Phys. B 546, 765 (1999)], and which was first thought to play the role of an "effective" central charge. The value of b has been determined over the last few years for the boundary versions of these models: $b_{\rm perco}=-5/8$ for percolation and $b_{\rm poly} = 5/6$ for dilute polymers. Meanwhile, the existence and value of $b$ for the bulk theory has remained an open problem. Using lattice regularization techniques we provide here an "experimental study" of this question. We show that, while the chiral stress tensor has indeed a single logarithmic partner in the chiral sector of the theory, the value of b is not the expected one: instead, b=-5 for both theories. We suggest a theoretical explanation of this result using operator product expansions and Coulomb gas arguments, and discuss the physical consequences on correlation functions. Our results imply that the relation between bulk LCFTs of physical interest and their boundary counterparts is considerably more involved than in the non-logarithmic case.