Electric-magnetic duality and topological order on the lattice (2010)
Buerschaper, Oliver, Christandl, Matthias, Kong, Liang, Aguado, Miguel
Dualities are deep conceptual tools in many areas of physics and mathematics; in particular, electric-magnetic (EM) duality has a long tradition ranging from Dirac's magnetic poles to S-duality in...
Invertible defects and isomorphisms of rational CFTs (2010)
Davydov, Alexei, Kong, Liang, Runkel, Ingo
Given two two-dimensional conformal field theories, a domain wall -- or defect line -- between them is called invertible if there is another defect with which it fuses to the identity defect. A...
Algebraic Structures in Euclidean and Minkowskian Two-Dimensional Conformal Field Theory (2009)
We review how modular categories, and commutative and non-commutative Frobenius algebras arise in rational conformal field theory. For Euclidean CFT we use an approach based on sewing of surfaces,...
ALGEBRAIC STRUCTURES IN EUCLIDEAN AND MINKOWSKIAN TWO-DIMENSIONAL CONFORMAL FIELD THEORY (2009)
Liang Kong, Ingo Runkel, Liang Kong, Ingo Runkel
We review how modular categories, and commutative and non-commutative Frobenius algebras arise in rational conformal field theory. For Euclidean CFT we use an approach based on sewing of surfaces,...
Cardy algebras and sewing constraints, I (2008)
This is part one of a two-part work that relates two different approaches to two-dimensional open-closed rational conformal field theory. In part one we review the definition of a Cardy algebra,...
Morita classes of algebras in modular tensor categories (2007)
We consider algebras in a modular tensor category C. If the trace pairing of an algebra A in C is non-degenerate we associate to A a commutative algebra Z(A), called the full centre, in a doubled...
Cardy condition for open-closed field algebras (2006)
Let $V$ be a vertex operator algebra satisfying certain reductivity and finiteness conditions such that $\mathcal{C}_V$, the category of V-modules, is a modular tensor category. We study open-closed...
Open-closed field algebras (2006)
We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we...
Modular invariance for conformal full field algebras (2006)
Let V^L and V^R be simple vertex operator algebras satisfying certain natural uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let F be a conformal full field algebra over...
Full field algebras, operads and tensor categories (2006)
We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted $\R\times \R$-graded full field algebra is equivalent to an...
We solve the problem of constructing a genus-zero full conformal field theory (a conformal field theory on genus-zero Riemann surfaces containing both chiral and antichiral parts) from...
World Journal of Modelling and Simulation (2005)
Liang Kong, Baolin Liu, Dehua Li, Yingliang Song, Aijun Zhang, Faning Dang, ...
Comparative study of 12 thread shapes of dental implant designs: a three-dimensional finite element analysis
Open-string vertex algebras, tensor categories and operads (2003)
We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the...