Virasoro Algebras With Central Charge $c < 1$

Bowcock, P.; Goddard, P.

doi:10.1016/0550-3213(87)90360-9

Virasoro Algebras With Central Charge $c < 1$

P. Bowcock
(
- Santa Barbara, KITP and
- Cambridge U.
)
,
P. Goddard
(
- Santa Barbara, KITP and
- Cambridge U.
)

Feb 10, 1987

29 pages

Published in:

Nucl.Phys.B 285 (1987) 651

DOI:

10.1016/0550-3213(87)90360-9

Report number:

PRINT-87-0123 (CAMBRIDGE),
NSF-ITP-87-13

View in:

AMS MathSciNet

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Abstract: (Elsevier)

It is known that, given an algebra and a subalgebra, g ⊃ h, the difference of the Sugawara constructions of the Virasoro algebras associated with the corresponding Kac-Moody algebras ĝ ⊃ ĥ defines another Virasoro algebra, v̂, and also that if the central charge of c of v̂ is less than 1, ĝ is finitely reducible with respect to ĥ ⊕ v̂. The converse, that finite reducibility implies c < 1, is shown to hold. The construction is shown to lead to relationships between the modular transformation properties of characters of the Virasoro and Kac-Moody algebras and the relevance of this to the construction of modular invariants is discussed. A complete list of cases for which c < 1 is given.

ALGEBRA: VIRASORO
ALGEBRA: CENTRAL CHARGE
ALGEBRA: KAC-MOODY
ALGEBRA: REPRESENTATION
TRANSFORMATION: REPARAMETRIZATION
FIELD THEORY: CONFORMAL

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Virasoro Algebras With Central Charge c<1c < 1c<1

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Virasoro Algebras With Central Charge $c < 1$