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

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: $b_{\mathrm{perco}}=-5/8$ for percolation and $b_{\mathrm{poly}}=5/6$ 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.

5 pages, published version

References in corpus (8)

• Associative-algebraic approach to logarithmic conformal field theories
• Enlarged symmetry algebras of spin chains, loop models, and S-matrices
• From Percolation to Logarithmic Conformal Field Theory
• Indecomposability parameters in chiral Logarithmic Conformal Field Theory
• A modular invariant bulk theory for the c=0 triplet model
• Twist operator correlation functions in O(n) loop models
• Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model
• Towards the Construction of Local Logarithmic Conformal Field Theories

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