String theory on group manifolds

Gepner, Doron; Witten, Edward

doi:10.1016/0550-3213(86)90051-9

Cited by 718 publications

(584 citation statements)

References 10 publications

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“…If the interaction picture is consistent, one must find that a tensor product between two allowed representations yields another allowed representation. One indication that this could be true is that for the auxiliaryĥ ′ -sector tensor products between integrable representations yield integrable representations [28]. Then BRST invariance would enforce that only antidominant integral weights can occur for theĝ-sector, ensuring consistency.…”

Section: Discussionmentioning

confidence: 99%

On the unitarity of gauged non-compact WZNW strings

Björnsson

Hwang

2008

Nuclear Physics B

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In this paper we investigate the unitarity of gauged non-compact WZNW strings i.e. string theories formulated as G/H ′ WZNW models, where G is a non-compact group. These models represent string theories on non-trivial curved space-times with one time-like component. We will prove that for the class of models connected to Hermitian symmetric spaces, and a natural set of discrete highest weight representations, the BRST formulation, in which the gauging is defined through a BRST condition, yields unitarity. Unitarity requires the level times the Dynkin index to be an integer, as well as integer valued highest weights w.r.t. the compact subalgebra. We will also show that the BRST formulation is not equivalent to the conventional GKO coset formulation, defined by imposing a highest weight condition w.r.t. H ′ . The latter leads to non-unitary physical string states. This is, to our knowledge, the first example of a fundamental difference between the two formulations.

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Section: Discussionmentioning

confidence: 99%

On the unitarity of gauged non-compact WZNW strings

Björnsson

Hwang

2008

Nuclear Physics B

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“…In this regime the α ′ -perturbation theory is applicable. Since in this limit, k ≫ N , the affine cutoff [34] is not visible when we consider representations with ∼ O(N ) columns in the Young tableau or less. Therefore, the fusion algebra of such low-lying representations is "perturbative": it coincides with the classical Glebsch-Gordan decomposition.…”

Section: Jhep04(2011)113mentioning

confidence: 99%

Large-N limits of 2d CFTs, quivers and AdS3 duals

Kiritsis

Niarchos

2011

J. High Energ. Phys.

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Abstract:We explore the large-N limits of 2d CFTs, focusing mostly on WZW models and their cosets. The SU(N ) k theory is parametrized in this limit by a 't Hooft-like coupling. We show a duality between strong coupling, where the theory is described by almost free fermions, and weak coupling where the theory is described by bosonic fields by an analysis of spectra and correlators. The AdS 3 dual is described, and several quantitative checks are performed. Besides the more standard states that should correspond to bulk black holes we find ground states with large degeneracy that can dominate the standard Cardy entropy at weak coupling and are expected to correspond to regular horizonless semiclassical bulk solutions.

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“…In this section we will just discuss the point-particle limit (or minisuperspace approximation) where only the zero-modes are taken into account and every dependence on the world-sheet coordinates is ignored. This corresponds to quantum mechanics on the supergroup [58]. Our aim is to find all the eigenfunctions of the Laplace (or wave) operator.…”

Section: Symmetrymentioning

confidence: 99%

Free fermion resolution of supergroup WZNW models

Quella

Schomerus²

2007

J. High Energy Phys.

132

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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.

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String theory on group manifolds

Cited by 718 publications

References 10 publications

On the unitarity of gauged non-compact WZNW strings

On the unitarity of gauged non-compact WZNW strings

Large-N limits of 2d CFTs, quivers and AdS3 duals

Free fermion resolution of supergroup WZNW models

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