Integrable quantum field theories with supergroup symmetries: The OSP (1/2) case

Saleur, Hubert; Wehefritz Kaufmann, Birgit

doi:10.1016/S0550-3213(03)00385-7

Integrable quantum field theories with supergroup symmetries: The OSP (1/2) case

Hubert Saleur
(
- Southern California U. and
- Saclay
)
,
Birgit Wehefritz Kaufmann
(
- Southern California U. and
- Bonn U.
)

Feb, 2003

24 pages

Published in:

Nucl.Phys.B 663 (2003) 443

e-Print:

hep-th/0302144 [hep-th]

DOI:

10.1016/S0550-3213(03)00385-7

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Abstract:

As a step to understand general patterns of integrability in 1+1 quantum field theories with supergroup symmetry, we study in details the case of

OSP(1/2)

. Our results include the solutions of natural generalizations of models with ordinary group symmetry: the

UOSP(1/2)_{k}

WZW model with a current current perturbation, the

UOSP(1/2)

principal chiral model, and the

UOSP(1/2)\otimes UOSP(1/2)/UOSP(1/2)

coset models perturbed by the adjoint. Graded parafermions are also discussed. A pattern peculiar to supergroups is the emergence of another class of models, whose simplest representative is the

OSP(1/2)/OSP(0/2)

sigma model, where the (non unitary) orthosymplectic symmetry is realized non linearly (and can be spontaneously broken). For most models, we provide an integrable lattice realization. We show in particular that integrable

osp(1/2)

spin chains with integer spin flow to

UOSP(1/2)

WZW models in the continuum limit, hence providing what is to our knowledge the first physical realization of a super WZW model.

Note:

24 pages, 9 figures Journal-ref: Nucl. Phys. B 663 (2003) 443

11.10.-z
field theory: conformal
Wess-Zumino-Witten model
dimension: 2
group theory: OSp(1/2)
integrability
coset space
current algebra
operator product expansion
fermion: parastatistics

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