W algebras with two and three generators

Blumenhagen, R.; Flohr, M.; Kliem, A.; Nahm, W.; Recknagel, A.; Varnhagen, R.

doi:10.1016/0550-3213(91)90624-7

W algebras with two and three generators

Jul, 1990

35 pages

Part of $W$-Symmetry, 255-289

Published in:

Nucl.Phys.B 361 (1991) 255-289

Published: 1991

DOI:

10.1016/0550-3213(91)90624-7

Report number:

BONN-HE-90-05

View in:

AMS MathSciNet

reference search167 citations

Citations per year

Abstract: (Elsevier)

We construct all W -algebras of chiral fields which in addition to the energy-momentum density have a single generator of conformal dimension up to 8. Some of them were unexpected, which indicates that present conjectures concerning the classification of conformally invariant quantum field theories in two dimensions are rather incomplete. We also explicitly construct the W A 3 -algebra with generators of dimensions 2, 3, 4.

algebra: W(N)
algebra: representation
field theory: conformal
dimension: 2
symmetry: SU(1,1)
operator: algebra
algebra: Virasoro
numerical calculations: interpretation of experiments

References(18)

Figures(0)

Infinite Additional Symmetries in Two-Dimensional Conformal Quantum Field Theory

A.B. Zamolodchikov
(
- Moscow, ITEP
)

- Theor.Math.Phys. 65 (1985) 1205-1213,
- Teor.Mat.Fiz. 65 (1985) 347-359,
- In *Bouwknegt, P. (ed.), Schoutens, K. (ed.): W-symmetry* 221-229, and In *Itzykson, C. (ed.) et al.: Conformal invariance and applications to statistical mechanics* 104-112. Theor. Math. Phys. 65 (1985) 1205-1213
•
DOI:
- 10.1007/BF01036128

Systematic Construction of Conformal Theories with Higher Spin Virasoro Symmetries

- Nucl.Phys.B 318 (1989) 579-630
•
DOI:
- 10.1016/0550-3213(89)90633-0

- Commun.Math.Phys. 122 351

Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory

A.A. Belavin
(
- Landau Inst.
)
,
Alexander M. Polyakov
(
- Landau Inst.
)
,
A.B. Zamolodchikov
(
- CERN and
- Landau Inst.
)

- Nucl.Phys.B 241 (1984) 333-380,
- IN *ITZYKSON, C. (ED.) ET AL.: CONFORMAL INVARIANCE AND APPLICATIONS TO STATISTICAL MECHANICS* 5-52. (NUCL. PHYS. B241 (1984) 333-380) AND CERN GENEVA - TH. 3827 (84,REC.JUN.) 71 P. (SEE BOOK INDEX),
•
DOI:
- 10.1016/0550-3213(84)90052-X

EXTENDED CONFORMAL ALGEBRAS

Peter Bouwknegt
(
- Amsterdam U.
)

- Phys.Lett.B 207 (1988) 295,
•
DOI:
- 10.1016/0370-2693(88)90578-3

SPIN 4 CURRENT ALGEBRA

Ken-Ji Hamada
(
- KEK, Tsukuba
)
,
Masaru Takao
(
- KEK, Tsukuba
)

- Phys.Lett.B 209 (1988) 247,
- Phys.Lett.B 213 (1988) 564 (erratum)
•
DOI:
- 10.1016/0370-2693(88)90941-0

SPIN 4 CURRENT ALGEBRA

Ken-Ji Hamada
(
- KEK, Tsukuba
)
,
Masaru Takao
(
- KEK, Tsukuba
)

- Phys.Lett.B 209 (1988) 247,
- Phys.Lett.B 213 (1988) 564 (erratum)
•
DOI:
- 10.1016/0370-2693(88)90941-0

SPIN 4 EXTENDED CONFORMAL ALGEBRA

De-Hai Zhang
(
)

- Phys.Lett.B 232 (1989) 323-326
•
DOI:
- 10.1016/0370-2693(89)90751-X

Extensions of the Virasoro Algebra Constructed from Kac-Moody Algebras Using Higher Order Casimir Invariants

- Nucl.Phys.B 304 (1988) 348-370,
- In *Bouwknegt, P. (ed.), Schoutens, K. (ed.): W-symmetry* 493-515
•
DOI:
- 10.1016/0550-3213(88)90631-1

Coset Construction for Extended Virasoro Algebras

- Nucl.Phys.B 304 (1988) 371-391,
- In *Bouwknegt, P. (ed.), Schoutens, K. (ed.): W-symmetry* 516-536
•
DOI:
- 10.1016/0550-3213(88)90632-3

Local observables and particle statistics. 1

Sergio Doplicher
(
- Marseille U., Luminy
)
,
Rudolf Haag
(
- Hamburg U.
)
,
John E. Roberts
(
- Princeton U.
)

- Commun.Math.Phys. 23 (1971) 199-230
•
DOI:
- 10.1007/BF01877742

Local observables and particle statistics. 2

- Commun.Math.Phys. 35 (1974) 49-85
•
DOI:
- 10.1007/BF01646454

Superselection Sectors with Braid Group Statistics and Exchange Algebras. 1. General Theory

K. Fredenhagen
(
- Freie U., Berlin
)
,
Karl-Henning Rehren
(
- Freie U., Berlin
)
,
B. Schroer
(
- Freie U., Berlin
)

- Commun.Math.Phys. 125 (1989) 201
•
DOI:
- 10.1007/BF01217906

Quantum Mechanics of Fractional Spin Particles

Frank Wilczek
(
- Santa Barbara, KITP
)

- Phys.Rev.Lett. 49 (1982) 957-959
•
DOI:
- 10.1103/PhysRevLett.49.957

Extended Chiral Algebras and Modular Invariant Partition Functions

A.N. Schellekens
(
- CERN
)
,
S. Yankielowicz
(
- CERN
)

- Nucl.Phys.B 327 (1989) 673-703
•
DOI:
- 10.1016/0550-3213(89)90310-6

The ADE Classification of Minimal and A1(1) Conformal Invariant Theories

- Commun.Math.Phys. 113 (1987) 1
•
DOI:
- 10.1007/BF01221394

- Phys.Lett.B 512 88

Unitary Representations of the Virasoro and Supervirasoro Algebras

P. Goddard
(
- Cambridge U.
)
,
A. Kent
(
- Cambridge U.
)
,
David I. Olive
(
- Imperial Coll., London
)

- Commun.Math.Phys. 103 (1986) 105-119,
- IN *ITZYKSON, C. (ED.) ET AL.: CONFORMAL INVARIANCE AND APPLICATIONS TO STATISTICAL MECHANICS* 159-173. (COMMUN. MATH. PHYS. 103 (1986) 105-119) AND CAMBRIDGE UNIV. - DAMTP 85-21 (85,REC.NOV.) 31 P. (SEE BOOK INDEX)
•
DOI:
- 10.1007/BF01464283