Showing papers on "Logarithmic conformal field theory published in 2021"
TL;DR: In particular, the authors showed that the category of all such twisted V-modules is a braided G-crossed (super) category, and that the G-equivariantization of this braided tensor equivalent to the original V-algebra is a BRAIDED tensor equivalence.
Abstract: A two-dimensional chiral conformal field theory can be viewed mathematically as the representation theory of its chiral algebra, a vertex operator algebra. Vertex operator algebras are especially well suited for studying logarithmic conformal field theory (in which correlation functions have logarithmic singularities arising from non-semisimple modules for the chiral algebra) because of the logarithmic tensor category theory of Huang, Lepowsky, and Zhang. In this paper, we study not-necessarily-semisimple or rigid braided tensor categories $${\mathcal {C}}$$
of modules for the fixed-point vertex operator subalgebra $$V^G$$
of a vertex operator (super)algebra V with finite automorphism group G. The main results are that every $$V^G$$
-module in $${\mathcal {C}}$$
with a unital and associative V-action is a direct sum of g-twisted V-modules for possibly several $$g\in G$$
, that the category of all such twisted V-modules is a braided G-crossed (super)category, and that the G-equivariantization of this braided G-crossed (super)category is braided tensor equivalent to the original category $${\mathcal {C}}$$
of $$V^G$$
-modules. This generalizes results of Kirillov and Muger proved using rigidity and semisimplicity. We also apply the main results to the orbifold rationality problem: whether $$V^G$$
is strongly rational if V is strongly rational. We show that $$V^G$$
is indeed strongly rational if V is strongly rational, G is any finite automorphism group, and $$V^G$$
is $$C_2$$
-cofinite.
14 citations
Posted Content•
TL;DR: In this paper, the scaling limits of Peano curves in the uniform spanning tree in topological polygons with general boundary conditions are given by certain variants of the SLE$_\kappa$ with $\kappa=8".
Abstract: We give a direct probabilistic construction for correlation functions in a logarithmic conformal field theory (log-CFT) of central charge $-2$. Specifically, we show that scaling limits of Peano curves in the uniform spanning tree in topological polygons with general boundary conditions are given by certain variants of the SLE$_\kappa$ with $\kappa=8$. We also prove that the associated crossing probabilities have conformally invariant scaling limits, given by ratios of explicit SLE$_8$ partition functions. These partition functions are interpreted as correlation functions in a log-CFT. Remarkably, it is clear from our results that this theory is not a minimal model and exhibits logarithmic phenomena --- indeed, the limit functions have logarithmic asymptotic behavior, that we calculate explicitly. General fusion rules for them could be inferred from the explicit formulas.
1 citations
TL;DR: In this paper, the authors consider the representation theory underlying the Nappi-Witten model and show that it is a logarithmic conformal field theory with finite-dimensional weight spaces over affine vertex operator algebra.
Abstract: The Nappi–Witten model is a Wess–Zumino–Witten model in which the target space is the nonreductive Heisenberg group $$H_4$$
. We consider the representation theory underlying this conformal field theory. Specifically, we study the category of weight modules, with finite-dimensional weight spaces, over the associated affine vertex operator algebra $$\mathsf {H}_4$$
. In particular, we classify the irreducible $$\mathsf {H}_4$$
-modules in this category and compute their characters. We moreover observe that this category is nonsemisimple, suggesting that the Nappi–Witten model is a logarithmic conformal field theory.
TL;DR: In this article, the authors present some examples of self-organized criticality (SOC) systems, and add some comments concerning its relation to logarithmic conformal field theory, and report on the application of SOC concepts to various systems ranging from cumulus clouds to 2D electron gases.
Abstract: This paper is devoted to the recent advances in self-organized criticality (SOC), and the concepts. The paper contains three parts; in the first part we present some examples of SOC systems, in the second part we add some comments concerning its relation to logarithmic conformal field theory, and in the third part we report on the application of SOC concepts to various systems ranging from cumulus clouds to 2D electron gases.
Posted Content•
TL;DR: In this article, the notion of a logarithmic vertex algebra is introduced, which is a vertex algebra with log-scale singularities in the operator product expansion of quantum fields.
Abstract: We introduce and study the notion of a logarithmic vertex algebra, which is a vertex algebra with logarithmic singularities in the operator product expansion of quantum fields; thus providing a rigorous formulation of the algebraic properties of quantum fields in logarithmic conformal field theory. We develop a framework that allows many results about vertex algebras to be extended to logarithmic vertex algebras, including in particular the Borcherds identity and Kac Existence Theorem. Several examples are investigated in detail, and they exhibit some unexpected new features that are peculiar to the logarithmic case.
Posted Content•
TL;DR: In this article, the authors consider a loop representation of the SLE model at the critical point when the model represents ensembles of self-avoiding loops (i.e., it corresponds to SLE with $\kappa=8/3$), and can be described by the logarithmic conformal field theory (LCFT) with central charge.
Abstract: We consider a loop representation of the $O(n)$ model at the critical point When $n=0$ the model represents ensembles of self-avoiding loops (ie, it corresponds to SLE with $\kappa=8/3$), and can be described by the logarithmic conformal field theory (LCFT) with central charge $c=0$ We focus on the correlation functions in the upper-half plane containing the twist operators in the bulk, and a pair of the boundary one-leg operators By using a Coulomb gas representation for the correlation functions, we obtain explicit results for probabilities of the SLE${}_{8/3}$ trace to wind in various ways about $N\geq 1$ marked points When the points collapse pairwise the probabilities reduce to multi-point Green's functions We propose an explicit representation for the Green's functions in terms of the correlation functions of the bulk 1/3-weight operators, and a pair of the boundary one-leg operators