Finite and infinite symmetries in (2+1)-Dimensional field theory

Center for Theoretical Physics Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology Cambridge, Massachusetts 02139 U.S.A.
Nuclear Physics B - Proceedings Supplements (Impact Factor: 0.88). 11/1993; 33(3):104-113. DOI: 10.1016/0920-5632(93)90375-G

ABSTRACT We describe the role of SO(2,1) conformal symmetry in non-relativistic Chern-Simons theory and in effective field theories for the eikonal regime: how the symmetry acts, how it controls the nature of solutions, how it expands to an infinite group on the manifold of static solutions thereby rendering the static problem completly integrable.

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    • "In general dimensions, the Schrödinger spacetime (1.1) with z = 2 has the Galilean group in D − 3 spatial dimensions as isometry group. For z = 2, the isometry group is enhanced to the Schrödinger group, which is the non-relativistic version of the conformal group [57] [58] [59] [60] [61]. This symmetry governs many non-relativistic systems, such as unitary fermions, via the gauge/gravity duality [49]. "
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    ABSTRACT: We construct Schroedinger-like solutions of the Vasiliev higher spin theory in D>3 dimension. Symmetries of such solutions and the linearised equation of motion for the scalar on such backgrounds are analysed. We further propose Galilean invariant bosonic and fermionic field theories that could be dual to the two parity invariant higher spin theories on the Schroedinger-like background respectively. The discussion is phrased mainly in D=4 dimension, while similar constructions follow straightforwardly in higher dimensions.
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    • "A similar " gauging " of nonrelativistic spatial translations has been considered previously [12]. A subclass of (17) which does not change the flat metric has been considered in Ref. [13]. "
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    ABSTRACT: We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion. At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics. At the next-to-leading order there are two additional constants. We express various physical quantities through these constants.
    Annals of Physics 10/2005; 321(1). DOI:10.1016/j.aop.2005.11.001 · 3.07 Impact Factor
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    ABSTRACT: A many-body Schroedinger equation for non-Abelian Chern-Simons particles is obtained from both point-particle and field-theoretic pictures. We present a particle Lagrangian and a field-theoretic Lagrange density, and discuss their properties. Both are quantized by the symplectic method of Hamiltonian reduction. An [ital N]-body Schroedinger equation for the particles is obtained from both starting points. It is shown that the resulting interaction between particles can be replaced by nontrivial boundary conditions. Also, the equation is compared with the one given in the literature.
    Physical review D: Particles and fields 07/1994; 49(12):6778-6786. DOI:10.1103/PhysRevD.49.6778 · 4.86 Impact Factor
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