The large-N limit of extended conformal symmetries

Bakas, Ioannis

doi:10.1016/0370-2693(89)90525-x

Cited by 218 publications

(225 citation statements)

References 29 publications

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“…These configurations are mapped into each other by reparametrizations of the coordinates of the plane which preserve the area. This is the dynamical symmetry of classical incompressible fluids under area-preserving diffeomorphisms [26][27], whose algebra is called w ∞ [28]. In particular, the infinitesimal shape changes, which are the classical edge waves, can be produced by applying the w ∞ infinitesimal generators to the ground-state droplet configuration [29].…”

Section: Theories Of Edge Excitationsmentioning

confidence: 99%

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Stable hierarchical quantum Hall fluids as W1+∞ minimal models

Cappelli¹,

Trugenberger

Zemba

1995

Nuclear Physics B

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In this paper, we pursue our analysis of the W 1+∞ symmetry of the lowenergy edge excitations of incompressible quantum Hall fluids. These excitations are described by (1 + 1)-dimensional effective field theories, which are built by representations of the W 1+∞ algebra. Generic W 1+∞ theories predict many more fluids than the few, stable ones found in experiments. Here we identify a particular class of W 1+∞ theories, the minimal models, which are made of degenerate representations only -a familiar construction in conformal field theory. The W 1+∞ minimal models exist for specific values of the fractional conductivity, which nicely fit the experimental data and match the results of the Jain hierarchy of quantum Hall fluids. We thus obtain a new hierarchical construction, which is based uniquely on the concept of quantum incompressible fluid and is independent of Jain's approach and hypotheses. Furthermore, a surprising non-Abelian structure is found in the W 1+∞ minimal models: they possess neutral quark-like excitations with SU (m) quantum numbers and nonAbelian fractional statistics. The physical electron is made of anyon and quark excitations. We discuss some properties of these neutral excitations which could be seen in experiments and numerical simulations.

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Section: Theories Of Edge Excitationsmentioning

confidence: 99%

“…These vectors satisfy the rules 28) and can be used to build the lattice of roots and weights of SU(m) [40]. The simple roots α (a) and the fundamental weights Λ (a) are…”

Section: (327)mentioning

confidence: 99%

Stable hierarchical quantum Hall fluids as W1+∞ minimal models

Cappelli¹,

Trugenberger

Zemba

1995

Nuclear Physics B

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“…To such an RCFT 4 is applied the orbifold construction with respect to G, a discrete group of inner automorphisms 5 of A(Z m ), obtaining a class of RCFT extensions of the fully degenerate W (m) 1+∞ . In this paper, we show that our theory TM [14], characterized as the cyclic permutation 3 Where Z m is the rank m orthonormal lattice. 4 See Theorem 5.2 of [34].…”

Section: Introductionmentioning

confidence: 84%

“…1+∞ chiral algebra W 1+∞ is the unique nontrivial central extension [31,39] of the Lie algebra w ∞ [3] of the areapreserving diffeomorphisms on the circle; its representation theory was developed in [33,22,1].…”

Section: The W (M)mentioning

confidence: 99%

A new rational conformal field theory extension of the fully degenerate W_1+∞^(m)

Cristofano

Marotta

Niccoli

2006

J. High Energy Phys.

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A new Rational Conformal Field Theory extension of the fully degenerate W (m) 1+∞Gerardo Cristofano 1 , Vincenzo Marotta 1 , Giuliano Niccoli 2 AbstractWe found new identities among the Dedekind η-function, the characters of the W m algebra and those of the level 1 affine Lie algebra su(m) 1 . They allow to characterize the Z m -orbifold of the m-component free bosons u(1) Km,p (our theory TM) as an extension of the fully degenerate representations of W (m) 1+∞ . In particular, TM is proven to be a Γ θ -RCFT extension of the chiral fully degenerate W (m) 1+∞ .

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“…It is also well-known that the equations of motion of 2-dimensional non-linear sigma models with the target space as the area-preserving diffeomorphism of an auxiliary 2-surface [2][3][4][5][6] are identical to the the self-dual Einstein's equations written in the Plebañski form [7].…”

Section: Introductionmentioning

confidence: 99%

Kaluza-Klein formalism of general spacetimes

Yoon

1999

Physics Letters B

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I describe the Kaluza-Klein approach to general relativity of 4-dimensional spacetimes. This approach is based on the (2,2)-fibration of a generic 4-dimensional spacetime, which is viewed as a local product of a (1+1)-dimensional base manifold and a 2-dimensional fibre space. It is shown that the metric coefficients can be decomposed into sets of fields, which transform as a tensor field, gauge fields, and scalar fields with respect to the infinite dimensional group of the diffeomorphisms of the 2-dimensional fibre space. I discuss a few applications of this formalism.

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The large-N limit of extended conformal symmetries

Cited by 218 publications

References 29 publications

Stable hierarchical quantum Hall fluids as W1+∞ minimal models

Stable hierarchical quantum Hall fluids as W1+∞ minimal models

A new rational conformal field theory extension of the fully degenerate W_1+∞^(m)

Kaluza-Klein formalism of general spacetimes

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The large-N limit of extended conformal symmetries

Cited by 218 publications

References 29 publications

Stable hierarchical quantum Hall fluids as W1+∞ minimal models

Stable hierarchical quantum Hall fluids as W1+∞ minimal models

A new rational conformal field theory extension of the fully degenerate W1+∞(m)

Kaluza-Klein formalism of general spacetimes

Contact Info

Product

Resources

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A new rational conformal field theory extension of the fully degenerate W_1+∞^(m)