Article

# Finite and Infinite Symmetries in (2+1)-Dimensional Field Theory

06/1992; DOI: 10.1016/0920-5632(93)90375-G

Source: arXiv

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**ABSTRACT:**We attempt to generalize the AdS/CFT correspondence to non-relativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and compute some two-point correlators. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions.05/2008; - [Show abstract] [Hide abstract]

**ABSTRACT:**We study representations of the Schr\"odinger algebra in terms of operators in nonrelativistic conformal field theories. We prove a correspondence between primary operators and eigenstates of few-body systems in a harmonic potential. Using the correspondence we compute analytically the energy of fermions at unitarity in a harmonic potential near two and four spatial dimensions. We also compute the energy of anyons in a harmonic potential near the bosonic and fermionic limits.Physical review D: Particles and fields 07/2007; - [Show abstract] [Hide abstract]

**ABSTRACT:**We construct a superfield formulation for non-relativistic Chern-Simons-Matter theories with manifest dynamical supersymmetry. By eliminating all the auxiliary fields, we show that the simple action reduces to the one obtained by taking non-relativistic limit from the relativistic Chern-Simons-Matter theory proposed in the literature. As a further application, we give a manifestly supersymmetric derivation of the non-relativistic ABJM theory. Comment: 18 pagesLetters in Mathematical Physics 02/2009; · 2.42 Impact Factor

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