Conformal quantum field theory models in two dimensions having Z3 symmetry

Fateev, V.A.; Zamolodchikov, A. B.

doi:10.1016/0550-3213(87)90166-0

Cited by 503 publications

(414 citation statements)

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“…Actually, the degenerate W 1+∞ representations are equivalent to representations of the U(1) ⊗ W m algebra, where W m is the ZamolodchikovFateev-Lykyanov algebra at c = m − 1 [39]. The fusion rules of this algebra are isomorphic to the tensor product of representations of the SU(m) Lie algebra; thus the neutral excitations in these theories are quark-like and their statistics is non-Abelian.…”

Section: The Topological Order and Its Independence Of Impuritiesmentioning

confidence: 99%

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Modular invariant partition functions in the quantum Hall effect

1997

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We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard form of rational conformal field theories. In particular, it is invariant under modular transformations of the toroidal geometry made by the angular variable and the compact Euclidean time. The Jain series of plateaus have been described by two types of edge theories: the minimal models of the W 1+∞ algebra of quantum area-preserving diffeomorphisms, and their non-minimal version, the theories with U (1) × SU (m) 1 affine algebra. We find modular invariant partition functions for the latter models. Moreover, we relate the Wen topological order to the modular transformations and the Verlinde fusion algebra. We find new, non-diagonal modular invariants which describe edge theories with extended symmetry algebra; their Hall conductivities match the experimental values beyond the Jain series.

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Section: The Topological Order and Its Independence Of Impuritiesmentioning

confidence: 99%

“…. , m [39]. The m-ality is additive mod m, thus the fusion rules are closed for theories having all values of α, or a subset α = δ, 2δ, .…”

Section: B Minimal Model Non-invariant Partition Functionsmentioning

confidence: 99%

Modular invariant partition functions in the quantum Hall effect

1997

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“…The generators of the W-algebra are constructed out of the Heisenberg subalgebra s by generalizing the Sugawara construction. The generator W s ′ n with s ′ -grade mN [30] is a differential operator in x:…”

Section: W Constraintsmentioning

confidence: 99%

Generalized integrability and two-dimensional gravitation

Hollowood¹,

Miramontes²,

Sánchez-Guillén³

1993

Theor Math Phys

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“…The physical symmetry constituents are currents whose O.P.E (or different recipes), generate extensions of the conformal symmetry [47] - [49]:for this reason they are usually defined as "primary fields". Their equations of motion define the dynamics of the system and, since they are defined on a Riemann surface [50] - [52], they must be promoted to the status of geometrical objects. Since any physical investigation cannot be separated from any geometrical consideration, the same kind of symmetry arises in the context of writting down welldefined differential equations on Riemann surfaces [20] - [62].…”

Section: Introductionmentioning

confidence: 99%