Bosonic realization of a universal W-algebra and Z∞ parafermions

Bakas, Ioannis; Kiritsis, Elias

doi:10.1016/0550-3213(90)90600-i

Cited by 101 publications

(124 citation statements)

References 24 publications

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“…This limit has been studied previously in specific examples, in [38][39][40][41][42][43], in order to produce representations of the W ∞ algebra. In this limit c ≃ kN + O(1) (3.11) and in this sense it looks like the theory is reducing in this case to a vectorial large-N theory.…”

Section: The Simple Large-n Limitmentioning

confidence: 99%

“…In coset theories primary field dimensions can also be of the order of O 1 N as shown in [23,38,39]. Consider the coset…”

Section: Jhep04(2011)113mentioning

confidence: 99%

“…It was shown in [38,39] that one can construct a class of operators of dimension O (1) out of operators of the class C. The construction involves operators as in (3.20) and the limit m 1 = q 1 √ N , m 2 = q 2 √ N with q 1 , q 2 fixed. Such operators were shown to have abelian OPEs and generate the analogue of the discrete series operators in pp-wave CFTs as shown in [30][31][32].…”

Section: Jhep04(2011)113mentioning

confidence: 99%

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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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Section: The Simple Large-n Limitmentioning

confidence: 99%

“…In coset theories primary field dimensions can also be of the order of O 1 N as shown in [23,38,39]. Consider the coset…”

Section: Jhep04(2011)113mentioning

confidence: 99%

Section: Jhep04(2011)113mentioning

confidence: 99%

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

Kiritsis

Niarchos

2011

J. High Energ. Phys.

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“…For large value of k, c φ → 2 and the underlying W k algebra linearizes in the k → ∞ limit giving rise to the well known Z ∞ parafermionic realization of W ∞ [21].…”

Section: Explicit Realizationmentioning

confidence: 99%

Wk structure of A from covariant construction of Kac-Moody algebras

Marotta

1998

Nuclear Physics B

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W k structure underlying the transverse realization of SU(2) at level k is analyzed. Extension of the equivalence existing between covariant and lightcone gauge realization of affine Kac-Moody algebra to W k algebras is given. Higher spin generators related to parafermions are extracted from the operator product algebra of the generators and are showed to be written in terms of only one free boson compactified on a circle.

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“…For example, we saw above that in the ferromagnetic case, the Heisenberg chain goes to a scale invariant theory with dynamical critical exponent z = 2. On the other hand, the k → ∞ limit of the Z k parafermions is a c = 2 conformal (and Lorentz invariant) theory, Z ∞ , described in [44] (this theory is also W ∞ symmetric). Moreover, in the anti-ferromagnetic case, the Heisenberg theory is described by the su(2) 1 theory, but the k → ∞ limit of M(k + 2, k + 1) is an irrational CFT [45].…”

Section: The Su(2) Intmentioning

confidence: 99%

Anyonic Chains, Topological Defects, and Conformal Field Theory

Buican

Gromov

2017

Commun. Math. Phys.

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Abstract:Motivated by the three-dimensional topological field theory/two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, which can give rise to an enormously rich (and largely unexplored) space of two-dimensional critical theories in the thermodynamic limit. One remarkable feature of these systems is the appearance of non-local microscopic "topological symmetries" that descend to topological defects of the resulting CFTs. We derive various model-independent properties of these theories and of this topological symmetry/topological defect correspondence. For example, by studying precursors of certain twist and defect fields directly in the anyonic chains, we argue that (under mild assumptions) the two-dimensional CFTs correspond to particular modular invariants with respect to their maximal chiral algebras and that the topological defects descending from topological symmetries commute with these maximal chiral algebras. Using this map, we apply properties of defect Hilbert spaces to show how topological symmetries give a handle on the set of allowed relevant deformations of these theories. Throughout, we give a unified perspective that treats the constraints from discrete symmetries on the same footing as the constraints from topological ones.

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Bosonic realization of a universal W-algebra and Z∞ parafermions

Cited by 101 publications

References 24 publications

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

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

Wk structure of A from covariant construction of Kac-Moody algebras

Anyonic Chains, Topological Defects, and Conformal Field Theory

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