Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications
By J. Cardy. 2013
140 citations recorded by the source corpus.
We describe an approach to logarithmic conformal field theories as limits of sequences of ordinary conformal field theories with varying central charge c. Logarithmic behaviour arises from degeneracies in the spectrum of scaling dimensions at certain values of c. The theories we consider are all invariant under some internal symmetry group, and logarithmic behaviour occurs when the decomposition of the physical observables into irreducible operators becomes singular. Examples considered are quenched random magnets using the replica formalism, self-avoiding walks as the n → 0 limit of the O(n) model, and percolation as the limit Q → 1 of the Potts model. In these cases we identify logarithmic operators and pay particular attention to how the c → 0 paradox is resolved and how the b-parameter is evaluated. We also show how this approach gives information on logarithmic behaviour in the extended Ising model, uniform spanning trees and the O( − 2) model. Most of our results apply to general dimensionality. We also consider massive logarithmic theories and, in two dimensions, derive sum rules for the effective central charge and the b-parameter.
Subfields: Condensed Matter Physics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1260ca722e74d6c852089a03af056e08f264b47f
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In Condensed Matter Physics
- J. Ruhman
- B. Skinner
- Sthitadhi Roy
- Romain Vasseur
- H. Saleur
- A. Nahum
- Jesper Lykke Jacobsen
- A. Gainutdinov
In Geometry and Topology
- A. Gainutdinov
- Romain Vasseur
- Jesper Lykke Jacobsen
- H. Saleur
- N. Read
- A. Nahum
- T. Creutzig
- David Ridout
In Mathematical Physics
- H. Saleur
- A. Nahum
- Jesper Lykke Jacobsen
- Romain Vasseur
- B. Skinner
- Sthitadhi Roy
- A. Gainutdinov
- J. Ruhman
Citations in the corpus
- Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, background): “[86] J.”
- Logarithmic conformal field theory: a lattice approach (2013, methodology): “This point of view is discussed in the contribution of Cardy [27] in this issue.”