Parafermions from coset models

Bardakci, K.; Crescimanno, Michael; Rabinovici, Eliezer

doi:10.1016/0550-3213(90)90365-k

Cited by 120 publications

(186 citation statements)

References 22 publications

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“…It is the 'reduction' of the configuration space resulting from integration over the gauge fields A,Ā that is responsible for a complicated form of the transformation law between the 'CFT' and 'leading-order' schemes in the gauged WZW σ-models (in particular, this transformation involves dilaton terms of all orders in 1/k, see below). 5 The basic example is the SL(2, R)/R gauged WZW model (or D = 2 black hole) [30,65,66]. The (euclidean) background in the leading-order scheme…”

Section: 'Cft' and 'Leading-order' Schemesmentioning

confidence: 99%

Exact solutions of closed string theory

Tseytlin

1995

Class. Quantum Grav.

109

222

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Theoretical Physics Group, Blackett LaboratoryImperial College, London SW7 2BZ, U.K. AbstractWe review explicitly known exact D = 4 solutions with Minkowski signature in closed bosonic string theory. Classical string solutions with space-time interpretation are represented by conformal sigma models. Two large (intersecting) classes of solutions are described by gauged WZW models and 'chiral null models' (models with conserved chiral null current). The latter class includes plane-wave type backgrounds (admitting a covariantly constant null Killing vector) and backgrounds with two null Killing vectors (e.g., fundamental string solution). D > 4 chiral null models describe some exact D = 4 solutions with electromagnetic fields, for example, extreme electric black holes, charged fundamental strings and their generalisations. In addition, there exists a class of conformal models representing axially symmetric stationary magnetic flux tube backgrounds (including, in particular, the dilatonic Melvin solution). In contrast to spherically symmetric chiral null models for which the corresponding conformal field theory is not known explicitly, the magnetic flux tube models (together with some non-semisimple WZW models) are among the first examples of solvable unitary conformal string models with non-trivial D = 4 curved space-time interpretation. For these models one is able to express the quantum hamiltonian in terms of free fields and to find explicitly the physical spectrum and string partition function. To appear as a review in Classical and Quantum GravityMay 1995 ⋆ e-mail address: tseytlin@ic.ac.uk † On leave from Lebedev Physics Institute, Moscow, Russia. IntroductionString theory is a remarkable extension of General Relativity which is consistent at the quantum level. One of the important problems is to study the set of exact classical solutions to string equations of motion. This may clarify its formal aspects but also may be relevant for understanding the implications of string theory for cosmology and black holes (assuming that in certain regions, e.g., at small times/scales, the effective string coupling is small so that perturbative and non-perturbative corrections to string equations of motion can be ignored). To be able to address issues of singularities and strong field behavior one should determine not just solutions of the leading-order low-energy string effective equations derived under the assumption of small field gradients (|α ′ R| ≪ 1, etc.) but solutions that are exact to all orders in α ′ (i.e., the corresponding exact conformal σ-models), and, ultimately, how first-quantized string modes propagate in a given background (i.e., the underlying conformal field theories).

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Section: 'Cft' and 'Leading-order' Schemesmentioning

confidence: 99%

Exact solutions of closed string theory

Tseytlin

1995

Class. Quantum Grav.

109

222

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“…This notation reminds of the geometric cosets but it should be kept in mind that the latter are different from the conformal ones (gauged WZW) discussed here. Explicit forms of the corresponding backgrounds have been worked out in the literature for various values of d, both to lowest order in α ′ ∼ 1/k [13,14,15,16,17,18,19] and to all orders [20,21].…”

Section: Frw Hierarchies In String Theorymentioning

confidence: 99%

Parafermions, brane distributions and FRW hierarchies

Petropoulos

2007

Fortschritte der Physik

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I review a class of exact string backgrounds, which appear in hierarchies, where the boundary of the target space of an exact sigma model is itself the target space of another exact model. From the worldsheet viewpoint this is due to the existence of (1, 1) operators based on parafermions. From the target space side, it is reminiscent of the structure of maximally symmetric Friedmann-Robertson-Walker cosmological solutions, with broken homogeneity though. Cosmological evolution in this framework raises again the question of the nature of time in string theory.

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“…The two black hole models [7,6] are generated by axial and vector gaugings with respect to the time-like element t 0 of the sl(2, R) algebra. For the axial gauge transformations…”

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Causal Poisson brackets of the WZNW model and its coset theories

Ford

Jorjadze²,

Weigt

2001

Physics Letters B

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From the basic chiral and anti-chiral Poisson bracket algebra of the SL(2, R) WZNW model, non-equal time Poisson brackets are derived. Through Hamiltonian reduction we deduce the corresponding brackets for its coset theories.The analysis of WZNW models is usually reduced to a separate treatment of its chiral or Here we consider the SL(2, R) WZNW model together with its three cosets, the Liouville theory and both the euclidean and Minkowskian black hole models. The general solution of the WZNW equations of motion gives g(τ, σ) as a product of chiral and anti-chiral fields g(z) andḡ(z), where z = τ + σ,z = τ − σ are light cone coordinates.For periodic boundary conditions, the chiral and anti-chiral fields have the monodromiesWe use the following basis of the sl(2, R) algebraIt satisfies the relations t m t n = −η mn I + ǫ mn l t l , where I is the unit matrix, η mn = diag(+, −, −) the metric tensor of 3d Minkowski space, and ǫ 012 = 1. For the matrices t n 1 email: ford@ifh.de 2

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Parafermions from coset models

Cited by 120 publications

References 22 publications

Exact solutions of closed string theory

Exact solutions of closed string theory

Parafermions, brane distributions and FRW hierarchies

Causal Poisson brackets of the WZNW model and its coset theories

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