From CFT to graphs

Petkova, V.B.; Zuber, J.B.

doi:10.1016/0550-3213(95)00670-2

From CFT to graphs

V.B. Petkova
(
- Clausthal, Tech. U. and
- Sofiya, Inst. Nucl. Res.
)
,
J.B. Zuber
(
- Saclay
)

Oct, 1995

38 pages

Published in:

Nucl.Phys.B 463 (1996) 161-193

e-Print:

hep-th/9510175 [hep-th]

DOI:

10.1016/0550-3213(95)00670-2

Report number:

ASI-TPA-014-95,
SACLAY-SPH-T-95-118

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Abstract:

In this paper, we pursue the discussion of the connections between rational conformal field theories (CFT) and graphs. We generalize our recent work on the relations of operator product algebra (OPA) structure constants of

sl(2)\,

theories with the Pasquier algebra attached to the graph. We show that in a variety of CFT built on

sl(n)\,

-- typically conformal embeddings and orbifolds, similar considerations enable one to write a linear system satisfied by the matrix elements of the Pasquier algebra in terms of conformal data -- quantum dimensions and fusion coefficients. In some cases, this provides a sufficient information for the determination of all the eigenvectors of an adjacency matrix, and hence of a graph.

Note:

44 pages, 6 postscript figures, the whole uuencoded. TEX file, macros used : harvmac.tex , epsf.tex. Optionally, AMS fonts in amssym.def and amssym.tex Report-no: ASI-TPA/14/95, SPhT 95/118

11.10.Kk
02.10.Tq
field theory: conformal
field theory: rational
dimension: 2
partition function
group theory: representation
graph theory

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