Tensor products of psl(2|2) representations - INSPIRE

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Tensor products of psl(2|2) representations

Gerhard Gotz
(
- Saclay, SPhT
)
,
Thomas Quella
(
- King's Coll. London
)
,
Volker Schomerus
(
- Saclay, SPhT and
- DESY
)

Jun, 2005

29 pages

e-Print:

hep-th/0506072 [hep-th]

Report number:

SPHT-T05-080,
KCL-MTH-05-05,
DESY-05-092

View in:

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Abstract:

The aim of this work is to study finite dimensional representations of the Lie superalgebra psl(2|2) and their tensor products. In particular, we shall decompose all tensor products involving typical (long) and atypical (short) representations as well as their so-called projective covers. While tensor products of long multiplets and projective covers close among themselves, we shall find an infinite family of new indecomposables in the tensor products of two short multiplets. Our note concludes with a few remarks on possible applications to the construction of AdS_3 backgrounds in string theory.

algebra: Lie
supersymmetry: algebra
algebra: psl(2/2)
algebra: representation
tensor

References(23)

Figures(0)

The GS string action on AdS(3) x S(3) with Ramond-Ramond charge

- Phys.Rev.D 60 (1999) 064014
•
e-Print:
- hep-th/9809164
•
DOI:
- 10.1103/PhysRevD.60.064014

Conformal field theory of AdS background with Ramond-Ramond flux

Nathan Berkovits
(
- Sao Paulo, IFT
)
,
Cumrun Vafa
(
- Harvard U.
)
,
Edward Witten
(
- Princeton, Inst. Advanced Study
)

- JHEP 03 (1999) 018
•
e-Print:
- hep-th/9902098
•
DOI:
- 10.1088/1126-6708/1999/03/018

Conformal field theory of the integer quantum Hall plateau transition

Martin R. Zirnbauer
(
- Princeton U.
)

e-Print:
- hep-th/9905054

Lie Superalgebras

V.G. Kac
(
- MIT, LNS
)

- Adv.Math. 26 (1977) 8-96
•
DOI:
- 10.1016/0001-8708(77)90017-2

- Commun.Algebra 5 889

Irreducible Representations of the OSP(2,1) and SPL(2,1) Graded Lie Algebras

- J.Math.Phys. 18 (1977) 155
•
DOI:
- 10.1063/1.523149

The Representations of Spl(2,1): An Example of Representations of Basic Superalgebras

M. Marcu
(
- Bonn U.
)

- J.Math.Phys. 21 (1980) 1277
•
DOI:
- 10.1063/1.524576

- J.Algebra 209 367

Dictionary on Lie superalgebras

L. Frappat
(
- Annecy, LAPP
)
,
P. Sorba
(
- Annecy, LAPP
)
,
A. Sciarrino
(
- Naples U. and
- INFN, Naples
)

e-Print:
- hep-th/9607161

The Tensor Product of Two Irreducible Representations of the Spl(2,1) Superalgebra

M. Marcu
(
- Bonn U.
)

- J.Math.Phys. 21 (1980) 1284
•
DOI:
- 10.1063/1.524577

Young Supertableaux of the Basic Lie Superalgebras

J.P. Hurni
(
- Geneva U.
)

- J.Phys.A 20 (1987) 5755
•
DOI:
- 10.1088/0305-4470/20/17/016

S and T matrices for the superU(1,1) WZW model: Application to surgery and three manifolds invariants based on the Alexander-Conway polynomial

L. Rozansky
(
- Texas U.
)
,
H. Saleur
(
- Yale U.
)

- Nucl.Phys.B 389 (1993) 365-423
•
e-Print:
- hep-th/9203069
•
DOI:
- 10.1016/0550-3213(93)90326-K

Representation theory of sl(2|1)

Gerhard Gotz
(
- Saclay, SPhT
)
,
Thomas Quella
(
- King's Coll. London
)
,
Volker Schomerus
(
- Saclay, SPhT
)

- J.Algebra 312 (2007) 829-848
•
e-Print:
- hep-th/0504234
•
DOI:
- 10.1016/j.jalgebra.2007.03.012

- J.Math.Phys. 41 5064

Type IIB superstring action in AdS(5) x S**5 background

R.R. Metsaev
(
- Lebedev Inst.
)
,
Arkady A. Tseytlin
(
- Lebedev Inst. and
- Imperial Coll., London and
- Santa Barbara, KITP
)

- Nucl.Phys.B 533 (1998) 109-126
•
e-Print:
- hep-th/9805028
•
DOI:
- 10.1016/S0550-3213(98)00570-7

PSL(n|n) sigma model as a conformal field theory

M. Bershadsky
(
- Harvard U.
)
,
Slava Zhukov
(
- Harvard U.
)
,
Arkady Vaintrob
(
- New Mexico State U.
)

- Nucl.Phys.B 559 (1999) 205-234
•
e-Print:
- hep-th/9902180
•
DOI:
- 10.1016/S0550-3213(99)00378-8

Superstring theory on AdS(2) x S**2 as a coset supermanifold

- Nucl.Phys.B 567 (2000) 61-86
•
e-Print:
- hep-th/9907200
•
DOI:
- 10.1016/S0550-3213(99)00683-5

Free fields and new cosets of current algebras

Itzhak Bars
(
- Southern California U.
)

- Phys.Lett.B 255 (1991) 353-358
•
DOI:
- 10.1016/0370-2693(91)90778-O

On structure constants and fusion rules in the SL(2,C) / SU(2) WZNW model

J. Teschner
(
- Montpellier U.
)

- Nucl.Phys.B 546 (1999) 390-422
•
e-Print:
- hep-th/9712256
•
DOI:
- 10.1016/S0550-3213(99)00072-3

Strings in AdS(3) and SL(2,R) WZW model 1.: The Spectrum

Juan Martin Maldacena
(
- Harvard U.
)
,
Hirosi Ooguri
(
- Caltech
)

- J.Math.Phys. 42 (2001) 2929-2960
•
e-Print:
- hep-th/0001053
•
DOI:
- 10.1063/1.1377273

Symplectic fermions

Horst G. Kausch
(
- Durham U., Dept. of Math.
)

- Nucl.Phys.B 583 (2000) 513-541
•
e-Print:
- hep-th/0003029
•
DOI:
- 10.1016/S0550-3213(00)00295-9

Branes in the Euclidean AdS(3)

B. Ponsot
(
- Potsdam, Max Planck Inst.
)
,
V. Schomerus
(
- Potsdam, Max Planck Inst. and
- Ecole Normale Superieure
)
,
J. Teschner
(
- Freie U., Berlin
)

- JHEP 02 (2002) 016
•
e-Print:
- hep-th/0112198
•
DOI:
- 10.1088/1126-6708/2002/02/016

Strings in AdS(3) and the SL(2,R) WZW model. Part 3. Correlation functions

Juan Martin Maldacena
(
- Harvard U. and
- Princeton, Inst. Advanced Study
)
,
Hirosi Ooguri
(
- Caltech
)

- Phys.Rev.D 65 (2002) 106006
•
e-Print:
- hep-th/0111180
•
DOI:
- 10.1103/PhysRevD.65.106006