668 research outputs found
Symplectic fermions and a quasi-Hopf algebra structure on
We consider the (finite-dimensional) small quantum group at
. We show that does not allow for an R-matrix, even
though holds for all finite-dimensional
representations of . We then give an explicit
coassociator and an R-matrix such that becomes a
quasi-triangular quasi-Hopf algebra.
Our construction is motivated by the two-dimensional chiral conformal field
theory of symplectic fermions with central charge . There, a braided
monoidal category, , has been computed from the factorisation and
monodromy properties of conformal blocks, and we prove that
is braided monoidally equivalent to
.Comment: 40pp, 11 figures; v2: few very minor corrections for the final
version in Journal of Algebr
A non-rational CFT with c=1 as a limit of minimal models
We investigate the limit of minimal model conformal field theories where the
central charge approaches one. We conjecture that this limit is described by a
non-rational CFT of central charge one. The limiting theory is different from
the free boson but bears some resemblance to Liouville theory. Explicit
expressions for the three point functions of bulk fields are presented, as well
as a set of conformal boundary states. We provide analytic and numerical
arguments in support of the claim that this data forms a consistent CFT.Comment: latex2e, 37 pages, 4 figure
The symplectic fermion ribbon quasi-Hopf algebra and the SL(2,Z)-action on its centre
We introduce a family of factorisable ribbon quasi-Hopf algebras for
a positive integer: as an algebra, is the semidirect product of
with the direct sum of a Grassmann and a Clifford
algebra in generators. We show that is ribbon equivalent to the
symplectic fermion category that was computed by the third author from
conformal blocks of the corresponding logarithmic conformal field theory. The
latter category in turn is conjecturally ribbon equivalent to representations
of , the even part of the symplectic fermion vertex operator super
algebra.
Using the formalism developed in our previous paper we compute the projective
-action on the centre of as obtained from
Lyubashenko's general theory of mapping class group actions for factorisable
finite ribbon categories. This allows us to test a conjectural non-semisimple
version of the modular Verlinde formula: we verify that the
-action computed from agrees projectively with that on
pseudo trace functions of .Comment: 75pp; typos fixed, references update
Reflection and Transmission for Conformal Defects
We consider conformal defects joining two conformal field theories along a
line. We define two new quantities associated to such defects in terms of
expectation values of the stress tensors and we propose them as measures of the
reflectivity and transmissivity of the defect. Their properties are
investigated and they are computed in a number of examples. We obtain a
complete answer for all defects in the Ising model and between certain pairs of
minimal models. In the case of two conformal field theories with an enhanced
symmetry we restrict ourselves to non-trivial defects that can be obtained by a
coset construction.Comment: 32 pages + 13 pages appendix, 12 figures; v2: added eqns (2.7), (2.8)
and refs [6,7,39,40], version published in JHE
Rite to Death, Left to Life: Death Ritual as a Cross-Cultural Unit of Analysis
Death ritual is a nearly ubiquitous aspect of life within civilization, and serves the purpose of reconciling the logical positivist societal constructions that uphold social order with the fundamentally logic-breaking nature of death. This paper posits that death ritual serves as a strong cross-cultural unit of analysis as it provides insight into the defining socio-cultural traits and spiritual outlooks of different cultures. This unit of analysis is applied to Song-era Ch’an Buddhism, pre-colonial Hindu India, and Maori death ritual. For each of these examples, death rites are connected to aspects of art, culture, social organization, and spirituality or religion, and they are examined in relation to one another. The paper concludes with a further analysis of the consistent role death ritual plays in maintaining positivist social systems while being adapted to the disparate cultural needs of a given society
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