Symplectic Fermions

By H. G. Kausch. 2000

210 citations recorded by the source corpus.

We study two-dimensional conformal field theories generated from a ``symplectic fermion'' - a free two-component fermion field of spin one - and construct the maximal local supersymmetric conformal field theory generated from it. This theory has central charge c=-2 and provides the simplest example of a theory with logarithmic operators. Twisted states with respect to the global SL(2,C)-symmetry of the symplectic fermions are introduced and we describe in detail how one obtains a consistent set of twisted amplitudes. We study orbifold models with respect to finite subgroups of SL(2,C) and obtain their modular invariant partition functions. In the case of the cyclic orbifolds explicit expressions are given for all two-, three- and four-point functions of the fundamental fields. The C_2-orbifold is shown to be isomorphic to the bosonic local logarithmic conformal field theory of the triplet algebra encountered previously. We discuss the relation of the C_4-orbifold to critical dense polymers.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7faf4f04c52557feacc19edeae2d45294b3f72fa

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Classification of irreducible modules of certain subalgebras of free boson vertex algebra (2002, background): “refore, the claim is veriﬁed, and the proof of the theorem is complete. Remark 3.2. If p = 2, then the elements E,F,H span the triplet algebra studied by M. Gaberdiel and H. Kausch (cf. [GK1], [GK2], [Ka2]). In this case M(1) is isomorphic to W–algebra W(2,3) with c = −2. Its irreducible modules wer”
The GL(1|1) WZW-model: From supergeometry to logarithmic CFT (2005, background): “ longer hesitate to write factors δ(0). After this brief digression into mathematical subtleties it is instructive to compare our answers forthe correlation functions of symplectic fermions (see e.g. [36]). The comparison shows that our typical vertex operators are very close relatives of the twist ”
Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and their Generalized Modules (2010, background): “nt years have attracted a lot of attention from physicists and mathematicians. Introduced by Kausch [K1], they have been studied extensively by Flohr [Fl1] [Fl2], Gaberdiel-Kausch [GK1] [GK3], Kausch [K2], Fuchs-HwangSemikhatov-Tipunin [FHST], Abe [Ab], Feigin-Ga˘ınutdinov-Semikhatov-Tipunin [FGST1]”
Logarithmic conformal field theory: beyond an introduction (2013, methodology): “The singlet algebrasM ( 1, p ) and triplet algebrasW ( 1, p ) , with p = 2,3, . . . and central chargec = 1−6(p−1)2/p, were first discovered by Kausch [26].”
Logarithmic extensions of minimal models: characters and modular transformations. (2006, background): “In accordance with the definition of the screening action in (4.1), the W±(z) currents can be written as (with normal ordering understood) W+(z) = P+3p+p−−3p+−p−+1 ep+α+ϕ(z), W−(z) = P−3p+p−−p+−3p−+1 e p−α−ϕ(z), whereP±j are polynomials of degreej in ∂nϕ, n> 1 (with deg ∂nϕ = n).”
An algebraic approach to logarithmic conformal field theory (2001, background): “One can show (see [59] for further details) that the bosonic sector of this representation is isomorphic to the representation R.”