Details
| Original language | English |
|---|---|
| Article number | P04002 |
| Journal | Journal of Statistical Mechanics: Theory and Experiment |
| Issue number | 4 |
| Publication status | Published - 12 Apr 2006 |
| Externally published | Yes |
Abstract
We examine the properties of two-dimensional conformal field theories (CFTs) with vanishing central charge based on the extended Kac table for c (9, 6) = 0 using a general ansatz for the stress energy tensor residing in a Jordan cell of rank two. Within this set-up we will derive the operator product expansions (OPEs) and two-point functions of the stress energy tensor T(z) and its logarithmic partner field t(z) and illustrate this by a bosonic field realization. We will show why our approach may be more promising than those chosen in the literature so far, including a discussion on properties of the augmented minimal model with vanishing central charge such as full conformal invariance of the vacuum as a state in an irreducible representation. Furthermore we will present a more general solution of another solution to the c → 0 catastrophe based on a logarithmic CFT tensor model. As an example, we consider a tensor product of the well known c = -2 logarithmic CFT with a fourfold Ising model. We give an overview of the possible configurations and various consequences for the two-point functions and the OPEs of the stress energy tensor T(z) and its logarithmic partner field t(z). We will motivate why, due to the full conformal invariance of the vacuum at c = 0, we should assume a Jordan cell for the identity, since t(z) is presumably a descendant of a new h = 0 field.
Keywords
- Conformal field theory, Disordered systems (theory), Percolation problems (theory)
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Journal of Statistical Mechanics: Theory and Experiment, No. 4, P04002, 12.04.2006.
Research output: Contribution to journal › Review article › Research › peer review
}
TY - JOUR
T1 - Notes on non-trivial and logarithmic conformal field theories with c = 0
AU - Flohr, Michael
AU - Müller-Lohmann, Annekathrin
PY - 2006/4/12
Y1 - 2006/4/12
N2 - We examine the properties of two-dimensional conformal field theories (CFTs) with vanishing central charge based on the extended Kac table for c (9, 6) = 0 using a general ansatz for the stress energy tensor residing in a Jordan cell of rank two. Within this set-up we will derive the operator product expansions (OPEs) and two-point functions of the stress energy tensor T(z) and its logarithmic partner field t(z) and illustrate this by a bosonic field realization. We will show why our approach may be more promising than those chosen in the literature so far, including a discussion on properties of the augmented minimal model with vanishing central charge such as full conformal invariance of the vacuum as a state in an irreducible representation. Furthermore we will present a more general solution of another solution to the c → 0 catastrophe based on a logarithmic CFT tensor model. As an example, we consider a tensor product of the well known c = -2 logarithmic CFT with a fourfold Ising model. We give an overview of the possible configurations and various consequences for the two-point functions and the OPEs of the stress energy tensor T(z) and its logarithmic partner field t(z). We will motivate why, due to the full conformal invariance of the vacuum at c = 0, we should assume a Jordan cell for the identity, since t(z) is presumably a descendant of a new h = 0 field.
AB - We examine the properties of two-dimensional conformal field theories (CFTs) with vanishing central charge based on the extended Kac table for c (9, 6) = 0 using a general ansatz for the stress energy tensor residing in a Jordan cell of rank two. Within this set-up we will derive the operator product expansions (OPEs) and two-point functions of the stress energy tensor T(z) and its logarithmic partner field t(z) and illustrate this by a bosonic field realization. We will show why our approach may be more promising than those chosen in the literature so far, including a discussion on properties of the augmented minimal model with vanishing central charge such as full conformal invariance of the vacuum as a state in an irreducible representation. Furthermore we will present a more general solution of another solution to the c → 0 catastrophe based on a logarithmic CFT tensor model. As an example, we consider a tensor product of the well known c = -2 logarithmic CFT with a fourfold Ising model. We give an overview of the possible configurations and various consequences for the two-point functions and the OPEs of the stress energy tensor T(z) and its logarithmic partner field t(z). We will motivate why, due to the full conformal invariance of the vacuum at c = 0, we should assume a Jordan cell for the identity, since t(z) is presumably a descendant of a new h = 0 field.
KW - Conformal field theory
KW - Disordered systems (theory)
KW - Percolation problems (theory)
UR - http://www.scopus.com/inward/record.url?scp=42749107537&partnerID=8YFLogxK
U2 - 10.48550/arXiv.hep-th/0510096
DO - 10.48550/arXiv.hep-th/0510096
M3 - Review article
AN - SCOPUS:42749107537
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
SN - 1742-5468
IS - 4
M1 - P04002
ER -