Continuum limit of the integrable superspin chain

Eßler, Fabian H. L.; Frahm, Holger; Saleur, Hubert

doi:10.1016/j.nuclphysb.2005.01.021

Cited by 60 publications

(140 citation statements)

References 88 publications

Supporting

Mentioning

122

Contrasting

Order By: Relevance

“…(2.11) seems to be overcome if one uses the approach of [50]. 7 The attribute "projective" is used here in the sense of category theory and should not be confused with the notion of projective representations that is used when algebraic relations are only respected up to some multipliers (cocycles). 8 It should be stressed that this property is not true for type II Lie superalgebras.…”

Section: Projective Modulesmentioning

confidence: 99%

Free fermion resolution of supergroup WZNW models

Quella

Schomerus²

2007

J. High Energy Phys.

132

View full text Add to dashboard Cite

Extending our earlier work on PSL(2|2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic subgroup. The new analysis covers in particular the supergroups GL(M |N ) along with several close relatives such as PSL(N |N ), certain Poincaré supergroups and the series OSP (2|2N ). The technical foundation for this remarkable progress is a special Feigin-Fuchs type representation which allows to keep the bosonic symmetry manifest instead of reducing it to free fields. In preparation for the field theory analysis, we shall exploit a minisuperspace analogue of the resulting free fermion construction to deduce the spectrum of the Laplacian on type I supergroups. The latter is shown to be non-diagonalizable. After lifting these results to the full WZNW model, we address various issues of the field theory, including its modular invariance and the computation of correlation functions. In agreement with previous findings, supergroup WZNW models allow to study chiral and non-chiral aspects of logarithmic conformal field theory within a geometric framework. We shall briefly indicate how insights from WZNW models carry over to non-geometric examples, such as e.g. the W(p) triplet models.

show abstract

Section: Projective Modulesmentioning

confidence: 99%

Free fermion resolution of supergroup WZNW models

Quella

Schomerus²

2007

J. High Energy Phys.

132

View full text Add to dashboard Cite

show abstract

“…For further string motivated research in this direction see e.g. [15,16,17], and for more condensed matter oriented work see [19,20,21,22]). …”

Section: Introductionmentioning

confidence: 99%

The WZW-model: From supergeometry to logarithmic CFT

2006

Self Cite

View full text Add to dashboard Cite

We present a complete solution of the WZW model on the supergroup GL(1|1). Our analysis begins with a careful study of its minisuperspace limit ("harmonic analysis on the supergroup"). Its spectrum is shown to contain indecomposable representations. This is interpreted as a geometric signal for the appearance of logarithms in the correlators of the full field theory. We then discuss the representation theory of the gl(1|1) current algebra and propose an Ansatz for the state space of the WZW model. The latter is established through an explicit computation of the correlation function. We show in particular, that the 4-point functions of the theory factorize on the proposed set of states and that the model possesses an interesting spectral flow symmetry. The note concludes with some remarks on generalizations to other supergroups.

show abstract

“…As a way out, one can try to 'discretize' the sigma model and construct a lattice spin chain of length N that would flow into the former in the continuum limit N → ∞. It has been proposed [10,11] to look for such models among integrable graded spin chains with the Hilbert space of the type (V ⊗V) ⊗N/2 with V andV being conjugated infinite-dimensional representations of supergroups. However, the tensor product V⊗V contains in general irreducible components which have neither the highest, nor the lowest weight vectors and, as a consequence, the nested Bethe ansatz is not applicable.…”

Section: Introductionmentioning

confidence: 99%

The BaxterQ-operator for the gradedSL(2|1) spin chain

Belitsky¹,

Derkachov²,

Korchemsky³

et al. 2007

J. Stat. Mech.

View full text Add to dashboard Cite

We study an integrable noncompact superspin chain model that emerged in recent studies of the dilatation operator in the N = 1 super-Yang-Mills theory. It was found that the latter can be mapped into a homogeneous Heisenberg magnet with the quantum space in all sites corresponding to infinite-dimensional representations of the SL(2|1) group. We extend the method of the Baxter Q−operator to spin chains with supergroup symmetry and apply it to determine the eigenspectrum of the model. Our analysis relies on a factorization property of the R−operators acting on the tensor product of two generic infinite-dimensional SL(2|1) representations. It allows us to factorize an arbitrary transfer matrix into a product of three 'elementary' transfer matrices which we identify as Baxter Q−operators. We establish functional relations between transfer matrices and use them to derive the TQ-relations for the Q−operators. The proposed construction can be generalized to integrable models based on supergroups of higher rank and, in distinction to the Bethe Ansatz, it is not sensitive to the existence of the pseudovacuum state in the quantum space of the model.

show abstract

Continuum limit of the integrable superspin chain

Cited by 60 publications

References 88 publications

Free fermion resolution of supergroup WZNW models

Free fermion resolution of supergroup WZNW models

The WZW-model: From supergeometry to logarithmic CFT

The BaxterQ-operator for the gradedSL(2|1) spin chain

Contact Info

Product

Resources

About