Trigonometric structure constants for new infinite-dimensional algebras

Fairlie, D.B.; Fletcher, P. Thomas; Zachos, Cosmas

doi:10.1016/0370-2693(89)91418-4

Cited by 238 publications

(202 citation statements)

References 11 publications

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“…The analogue of the T n generators in the SU(N) matrix model is a special basis of generators {J n } of the Lie algebra of SU(N) satisfying the algebra [30,31] […”

Section: Membranes Solutions and Matrix Model Solutionsmentioning

confidence: 99%

Nonperturbative states in type II superstring theory from classical spinning membranes

2005

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We find a new family of exact solutions in membrane theory, representing toroidal membranes spinning in several planes. They have energy square proportional to the sum of the different angular momenta, generalizing Regge-type string solutions to membrane theory. By compactifying the eleven dimensional theory on a circle and on a torus, we identify a family of new non-perturbative states of type IIA and type IIB superstring theory (which contains the perturbative spinning string solutions of type II string theory as a particular case). The solution represents a spinning bound state of D branes and fundamental strings. Then we find similar solutions for membranes on AdS 7 × S 4 and AdS 4 × S 7 . We also consider the analogous solutions in SU(N) matrix theory, and compute the energy. They can be interpreted as rotating open strings with D0 branes attached to their endpoints.

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“…The analogue of the T n generators in the SU(N) matrix model is a special basis of generators {J n } of the Lie algebra of SU(N) satisfying the algebra [30,31] […”

Section: Membranes Solutions and Matrix Model Solutionsmentioning

confidence: 99%

Nonperturbative states in type II superstring theory from classical spinning membranes

2005

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“…This algebra, the GMP algebra, [44][45][46][47][48] plays two crucial roles. First, within the SMA approximation, 33 it dictates under what conditions interactions open a spectral gap between the many-body interacting ground state and its excitations upon lowering the chemical potential within the first Landau level.…”

Section: Noncommutative Geometrymentioning

confidence: 99%

Noncommutative geometry for three-dimensional topological insulators

et al. 2012

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We generalize the noncommutative relations obeyed by the guiding centers in the two-dimensional quantum Hall effect to those obeyed by the projected position operators in three-dimensional (3D) topological band insulators. The noncommutativity in 3D space is tied to the integral over the 3D Brillouin zone of a Chern-Simons invariant in momentum-space. We provide an example of a model on the cubic lattice for which the chiral symmetry guarantees a macroscopic number of zero-energy modes that form a perfectly flat band. This lattice model realizes a chiral 3D noncommutative geometry. Finally, we find conditions on the density-density structure factors that lead to a gapped 3D fractional chiral topological insulator within Feynman's single-mode approximation.

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“…One can restrict to a fundamental lattice defined by n 1 , n 2 = 0, ..., N −1, with the exception of the origin n 1 = n 2 = 0, which label N 2 − 1 generators; these can be shown to span the algebra of SU (N ) [8]. Note that the Cartan subalgebra can be taken to be generated by J n , with n 1 = 0, n 2 = 1, ..., N − 1.…”

Section: Generalitiesmentioning

confidence: 99%

Supermembrane dynamics from multiple interacting strings

Russo

1997

Nuclear Physics B

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The supermembrane theory on R 10 × S 1 is investigated, for membranes that wrap once around the compact dimension. The Hamiltonian can be organized as describing N s interacting strings, the exact supermembrane corresponding to N s → ∞. The zero-mode part of N s − 1 strings turn out to be precisely the modes which are responsible of instabilities. For sufficiently large compactification radius R 0 , interactions are negligible and the lowest-energy excitations are described by a set of harmonic oscillators. We compute the physical spectrum to leading order, which becomes exact in the limit g 2 → ∞, where g 2 ≡ 4π 2 T 3 R 3 0 and T 3 is the membrane tension. As the radius is decreased, more strings become strongly interacting and their oscillation modes get frozen. In the zero-radius limit, the spectrum is constituted of the type IIA superstring spectrum, plus an infinite number of extra states associated with flat directions of the quartic potential.

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Trigonometric structure constants for new infinite-dimensional algebras

Cited by 238 publications

References 11 publications

Nonperturbative states in type II superstring theory from classical spinning membranes

Nonperturbative states in type II superstring theory from classical spinning membranes

Noncommutative geometry for three-dimensional topological insulators

Supermembrane dynamics from multiple interacting strings

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