Seven-sphere and the exceptional N = 7 and N = 8 superconformal algebras

Günaydın, Murat; Ketov, Sergei V.

doi:10.1016/0550-3213(96)00088-0

Cited by 32 publications

(55 citation statements)

References 71 publications

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“…This is to be contrasted with the realizations given above that lead to all allowed values of the central charges. 8 As argued in [18], the exceptional SCA's may arise as hidden symmetries in certain compactifications of superstring theories or of M-theory. They may also be relevant for a stringy description of the octonionic soliton solutions of heterotic string theory [34,35,36] and may underlie some exceptional superstring theories.…”

Section: Discussionmentioning

confidence: 99%

“…The realizations of QSCA's and SCA's with non-simple symmetry groups as well as those of SQSCA's will be given elsewhere [31]. The exceptional nonlinear N = 8 and N = 7 SCA's with Spin(7) and G 2 symmetry were studied in [18] using coset space methods. There, it was shown that there exist unique consistent realizations of these algebras over the coset spaces SO(8) × U (1)/SO(7) and SO(7) × U (1)/G 2 with central charges c = 84/11 and c = 5, respectively.…”

Section: Discussionmentioning

confidence: 99%

“…The realizations of the nonlinear SCA's with U (n) and SO(n) symmetry were studied in [16,17] and those of the exceptional N = 8 and N = 7 SCA's in [18]. The quantum Hamiltonian reduction can also be used to obtain W N algebras [19] of the type first introduced by Zamolodchikov [20].…”

Section: Introductionmentioning

confidence: 99%

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Real forms of non-linear superconformal and quasi-superconformal algebras and their unified realization

Bina

Günaydın

1997

Nuclear Physics B

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We give a complete classification of the real forms of simple nonlinear superconformal algebras (SCA) and quasi-superconformal algebras (QSCA) and present a unified realization of these algebras with simple symmetry groups. This classification is achieved by establishing a correspondence between simple nonlinear QSCA's and SCA's and quaternionic and superquaternionic symmetric spaces of simple Lie groups and Lie supergroups, respectively. The unified realization we present involves a dimension zero scalar field (dilaton), dimension-1 symmetry currents, and dimension-1/2 free bosons for QSCA's and dimension-1/2 free fermions for SCA's. The free bosons and fermions are associated with the quaternionic and superquaternionic symmetric spaces of corresponding Lie groups and Lie supergroups, respectively. We conclude with a discussion of possible applications of our results.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Real forms of non-linear superconformal and quasi-superconformal algebras and their unified realization

Bina

Günaydın

1997

Nuclear Physics B

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“…In the following we will design an interaction that separates the factors and leads to 2D topological phases with either c = 14/5 (Fibonacci) or c = 7/10 (anti-Fibonacci) edge states. We begin with some facts about G 2 , which is well known in mathematical physics [38,40]. G 2 is the simplest exceptional Lie group.…”

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confidence: 99%

Fibonacci Topological Superconductor

Kane

2018

Phys. Rev. Lett.

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We introduce a model of interacting Majorana fermions that describes a superconducting phase with a topological order characterized by the Fibonacci topological field theory. Our theory, which is based on a SO(7)1/(G2)1 coset factorization, leads to a solvable one dimensional model that is extended to two dimensions using a network construction. In addition to providing a description of the Fibonacci phase without parafermions, our theory predicts a closely related "anti-Fibonacci" phase, whose topological order is characterized by the tricritical Ising model. We show that Majorana fermions can split into a pair of Fibonacci anyons, and propose an interferometer that generalizes the Z2 Majorana interferometer and directly probes the Fibonacci non-Abelian statistics.Current interest in topological quantum phases is heightened by the proposal to use them for quantum information processing [1,2] and by prospects for realizing them in experimentally viable electronic systems. There is growing evidence that the fractional quantum Hall (QH) state at filling ν = 5/2 is a non-Abelian state [3][4][5][6][7] with Ising topological order. A simpler form of Ising order is predicted in topological superconductors (T-SC) [8,9] and in SC proximity effect devices [10][11][12][13][14]. In these systems the Ising σ particle is not dynamical, but is associated with domain walls or vortices that host gapless Majorana fermion modes. Recent experiments have found promising evidence for Majorana fermions in 1D and 2D SC systems [15][16][17].Ising topological order is insufficient for universal quantum computation, but the richer Fibonacci topological order is sufficient [18]. Fibonacci order arises in the Z 3 parafermion state introduced by Read and Rezayi[19], which is a candidate for the fractional QH state at ν = 12/5. Parafermions can also be realized by combining SC with the fractional QH effect [20][21][22][23][24]. This line of inquiry culminated in the tour de force works [25,26] that showed a ν = 2/3 QH state, appropriately proximitized, could exhibit a Fibonacci phase.In this paper we introduce a different formulation of the Fibonacci phase based on a model of interacting Majorana fermions. Our starting point is a system of chiral Majorana edge states, which can in principle be realized in SC proximity effect structures. We show that a particular four fermion interaction leads to an essentially exactly solvable model that realizes the Fibonacci phase. In addition to providing a direct route to the Fibonacci phase without parafermions, our theory reveals a distinct but closely related "anti-Fibonacci" state that is a kind of particle-hole conjugate to the Fibonacci state with a topological order that combines Ising and Fibonacci. Our formulation also suggests a method for experimentally probing the Fibonacci state. We introduce a generalization of the interferometer introduced earlier for Majorana states [27,28], and argue that it provides a method for unambiguously detecting Fibonacci order.The fact that interacting Majorana ...

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“…In this section we recall (see [14] and [11]) the basic properties of the division algebra of the octonions which will be used in the following and introduce the "Non-Associative N = 8 Superconformal Algebra" according to [8] (see also [11]). …”

mentioning

confidence: 99%

Division algebras and extendedN 2, 4, 8 superKdVs

Carrion¹,

Rojas²,

Toppan³

2003

J. Phys. A: Math. Gen.

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The first example of an N = 8 supersymmetric extension of the KdV equation is here explicitly constructed. It involves 8 bosonic and 8 fermionic fields. It corresponds to the unique N = 8 solution based on a generalized hamiltonian dynamics with (generalized) Poisson brackets given by the Non-associative N = 8 Superconformal Algebra. The complete list of inequivalent classes of parametric-dependent N = 3 and N = 4 superKdVs obtained from the "Non-associative N = 8 SCA" is also furnished. Furthermore, a fundamental domain characterizing the class of inequivalent N = 4 superKdVs based on the "minimal N = 4 SCA" is given.

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Seven-sphere and the exceptional N = 7 and N = 8 superconformal algebras

Cited by 32 publications

References 71 publications

Real forms of non-linear superconformal and quasi-superconformal algebras and their unified realization

Real forms of non-linear superconformal and quasi-superconformal algebras and their unified realization

Fibonacci Topological Superconductor

Division algebras and extendedN 2, 4, 8 superKdVs

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