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J. Fuchs

Publications and source records attributed to J. Fuchs.

89 records · Page 5Linked to original sources
arXiv1998

A representation theoretic approach to the WZW Verlinde formula

By exploring the description of chiral blocks in terms of co-invariants, a derivation of the Verlinde formula for WZW models is obtained which is entirely based on the representation theory of affine Lie algebras. In contrast to existing proofs of the Verlinde formula, this approach works universally for all untwisted affine Lie algebras. As a by-product we obtain a homological interpretation of the Verlinde multiplicities as Euler characteristics of complexes built from invariant tensors of finite-dimensional simple Lie algebras. Our results can also be used to compute certain traces of automorphisms on the spaces of chiral blocks. Our argument is not rigorous; in its present form this paper will therefore not be submitted for publication.

hep-th↗
arXiv1998

D-brane conformal field theory

We outline the structure of boundary conditions in conformal field theory. A boundary condition is specified by a consistent collection of reflection coefficients for bulk fields on the disk together with a choice of an automorphism ωof the fusion rules that preserves conformal weights. Non-trivial automorphisms ωcorrespond to D-brane configurations for arbitrary conformal field theories.

hep-th↗
arXiv1998

Branes: from free fields to general backgrounds

Motivated by recent developments in string theory, we study the structure of boundary conditions in arbitrary conformal field theories. A boundary condition is specified by two types of data: first, a consistent collection of reflection coefficients for bulk fields on the disk; and second, a choice of an automorphism $ω$ of the fusion rules that preserves conformal weights. Non-trivial automorphisms $ω$ correspond to D-brane configurations for arbitrary conformal field theories. The choice of the fusion rule automorphism $ω$ amounts to fixing the dimension and certain global topological features of the D-brane world volume and the background gauge field on it. We present evidence that for fixed choice of $ω$ the boundary conditions are classified as the irreducible representations of some commutative associative algebra, a generalization of the fusion rule algebra. Each of these irreducible representations corresponds to a choice of the moduli for the world volume of the D-brane and the moduli of the flat connection on it.

hep-th↗
arXiv1997

A classifying algebra for boundary conditions

We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer spin simple current, modular invariant), this classifying algebra contains the fusion algebra of the untwisted sector as a subalgebra. Proper treatment of fields in the twisted sector, so-called fixed points, leads to structures that are intriguingly close to the ones implied by modular invariance for conformal field theories on closed orientable surfaces.

hep-th↗
arXiv1997

CFT fusion rules, DHR gauge groups, and CAR algebras

It is demonstrated that several series of conformal field theories, while satisfying braid group statistics, can still be described in the conventional setting of the DHR theory, i.e. their superselection structure can be understood in terms of a compact DHR gauge group. Besides theories with only simple sectors, these include (the untwisted part of) c=1 orbifold theories and level two so(N) WZW theories. We also analyze the relation between these models and theories of complex free fermions.

hep-th↗
arXiv1997

Universal simple current vertex operators

We construct a vertex operator realization for the simple current primary fields of WZW theories which are based on simply laced affine Lie algebras g. This is achieved by employing an embedding of the integrable highest weight modules of g into the Fock space for a bosonic string compactified on the weight lattice of g. Our vertex operators are universal in the sense that a single expression for the vertex operator holds simultaneously for all positive integral values of the level of g.

hep-th↗
arXiv1996

Fixed point resolution in conformal field theory

We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of chiral algebras are investigated. A crucial role is played by the mathematical structures of twining characters and orbit Lie algebras.

hep-th↗
arXiv1996

Twining characters and orbit Lie algebras

We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.

hep-th↗
arXiv1995

The singularity structure of the Yang-Mills configuration space

The geometric description of Yang-Mills theories and their configuration space M is reviewed. The presence of singularities in M is explained and some of their properties are described. The singularity structure is analyzed in detail for structure group SU(2).

hep-th↗
arXiv1994

Quasi-Galois Symmetries of the Modular S-Matrix

The recently introduced Galois symmetries of RCFT are generalized, for the WZW case, to `quasi-Galois symmetries'. These symmetries can be used to derive a large number of equalities and sum rules for entries of the modular matrix S, including some that previously had been observed empirically. In addition, quasi-Galois symmetries allow to construct modular invariants and to relate S-matrices as well as modular invariants at different levels. They also lead us to an extremely plausible conjecture for the branching rules of the conformal embeddings of g into so(dim g).

hep-th↗
arXiv1994

Galois Modular Invariants of WZW Models

The set of modular invariants that can be obtained from Galois transformations is investigated systematically for WZW models. It is shown that a large subset of Galois modular invariants coincides with simple current invariants. For algebras of type B and D infinite series of previously unknown exceptional automorphism invariants are found.

hep-th↗
arXiv1994

On the quantum symmetry of rational field theories

We describe the role of Rational Hopf Algebras as the symmetries of rational field theories and discuss their relation with algebraic field theory, braided monoidal categories and modular fusion rule algebras.

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arXiv1993

Level-Rank Duality of WZW Theories and Isomorphisms of N=2 Coset Models

Mappings between certain infinite series of N=2 superconformal coset models are constructed. They make use of level-rank dualities for B, C and D type theories. While the WZW level-rank dualities do not constitute isomorphisms of the theories, they lead to level-rank dualities of N=2 coset models that preserve the cft properties in such a manner that the coset models related by duality are expected to be isomorphic as conformal field theories. The construction also gives some further insight in the nature of the resolution of field identification fixed points of coset theories.

hep-th↗
arXiv1993

Fusion rules in conformal field theory

Several aspects of fusion rings and fusion rule algebras, and of their manifestations in twodimensional (conformal) field theory, are described: diagonalization and the connection with modular invariance; the presentation in terms of quotients of polynomial rings; fusion graphs; various strategies that allow for a partial classification; and the role of the fusion rules in the conformal bootstrap programme.

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