The BRST formulation of G/H WZNW models

Hwang, Stephen; Rhedin, Henric

doi:10.1016/0550-3213(93)90165-l

Cited by 37 publications

(99 citation statements)

References 37 publications

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“…This approach uses the BRST symmetry to define the coset space. For compact algebras this was shown to yield the same result as the conventional GKO coset formulation using highest weight conditions [17]. In order to construct a nilpotent BRST charge one starts with the g WZNW model at level k and supplement it with an auxiliary sector, which is a h ′ WZNW model of levelκ = −κ − 2g ∨ h ′ , where κ = I h ′ ⊂g k. I h ′ ⊂g is the Dynkin index of the embedding…”

Section: The Brst Approachmentioning

confidence: 98%

“…A fact which makes the present situation more difficult is that theĥ ′ -sector has a highly reducible highest weight Verma module. Null states make it impossible to define a homotopy operator in the way that was done in [17]. We can, however, adapt the techniques to our case by focusing on the g-sector instead, as this Verma module is irreducible.…”

Section: Brst Invariant Statesmentioning

confidence: 99%

“…We will denote B (ĝ,ĥ ′ ⊕V ir) (τ, φ) the generalized branching function 5 . This definition was first introduced in [17] and extended in [26]. We also define another function, which we will call a signature function.…”

Section: Unitaritymentioning

confidence: 99%

“…In [17] a technique was introduced to be able to analyze the cohomology. This technique was an extension of techniques first used in the string context in [24].…”

Section: Brst Invariant Statesmentioning

confidence: 99%

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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: The Brst Approachmentioning

confidence: 98%

Section: Brst Invariant Statesmentioning

confidence: 99%

Section: Unitaritymentioning

confidence: 99%

“…In [17] a technique was introduced to be able to analyze the cohomology. This technique was an extension of techniques first used in the string context in [24].…”

Section: Brst Invariant Statesmentioning

confidence: 99%

See 2 more Smart Citations

On the unitarity of gauged non-compact WZNW strings

Björnsson

Hwang

2008

Nuclear Physics B

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“…It is believed that most rational models of CFT can be obtained from the cosets G/A corresponding to the embedding a ⊂ g. These models can be studied as gauge theories [43,44].…”

Section: Branching Functions and Coset Models Of Conformal Field Theorymentioning

confidence: 99%

Affine.m—Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

Nazarov¹

2012

Computer Physics Communications

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In this paper we present Affine.m -a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most important problems for us. These problems have numerous applications in physics and we provide some examples of these applications. The program is implemented in the popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras. Keywords:Mathematica; Lie algebra; affine Lie algebra; Kac-Moody algebra; root system; weights; irreducible modules, CFT, Integrable systems Representation theory of finite-dimensional Lie algebras has many applications in different branches of physics, including elementary particle physics, molecular physics, nuclear physics. Representations of affine Lie algebras appear in string theories and two-dimensional conformal field theory used for the description of critical phenomena in two-dimensional systems. Also Lie symmetries play major role in a study of quantum integrable systems. PROGRAM SUMMARY Solution method:We work with weights and roots of finite-dimensional and affine Lie algebras and use Weyl symmetry extensively. Central problems which are the computations of weight multiplicities, branching and fusion coefficients are solved using one general recurrent algorithm based on generalization of Weyl character formula. We also offer alternative implementation based on the Freudenthal multiplicity formula which can be faster in some cases. Restrictions:Computational complexity grows fast with the rank of an algebra, so computations for algebras of ranks greater than 8 are not practical. Unusual features:We offer the possibility to use a traditional mathematical notation for the objects in representation theory of Lie algebras in computations if Affine.m is used in the Mathematica notebook interface. Running time:From seconds to days depending on the rank of the algebra and the complexity of the representation.2

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String theory on warped AdS3 and Virasoro resonances

Detournay

Israël

Lapan

et al. 2011

J. High Energ. Phys.

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We investigate aspects of holographic duals to time-like warped AdS 3 spacetimes -which include Gödel's universe -in string theory. Using worldsheet techniques similar to those that have been applied to AdS 3 backgrounds, we are able to identify spacetime symmetry algebras that act on the dual boundary theory. In particular, we always find at least one Virasoro algebra with computable central charge. Interestingly, there exists a dense set of points in the moduli space of these models in which there is actually a second commuting Virasoro algebra, typically with different central charge than the first. We analyze the supersymmetry of the backgrounds, finding related enhancements, and comment on possible interpretations of these results. We also perform an asymptotic symmetry analysis at the level of supergravity, providing additional support for the worldsheet analysis.

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The BRST formulation of G/H WZNW models

Cited by 37 publications

References 37 publications

On the unitarity of gauged non-compact WZNW strings

On the unitarity of gauged non-compact WZNW strings

Affine.m—Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

String theory on warped AdS3 and Virasoro resonances

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