Nonrelativistic conformal field theories

By Y. Nishida, D. Son. 2007

340 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/7befeb3645287c4583051ede55633741ccf29439

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Gravity duals for nonrelativistic conformal field theories. (2008, background): “which appears in [ 7 ] (related work includes [9]).”
Gravity duals for non-relativistic CFTs (2008, methodology): “The familiar Schrödinger case has z = 2, and the conformal algebra for this case is described in [7].”
On instantons as Kaluza-Klein modes of M5-branes (2011, background): “J H E P 1 2 ( 2 0 1 1 ) 0 3 1 As explained in [55], local eigen-operators of the dilatation operator D can be mapped to the eigenstates of L0.”
Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, background): “Furthermore, in the case z = 2 arising in cold fermions at unitarity, the symmetry algebra is enlarged [383] and includes a central Number operator, N̂ , such that every operator has, in addition to a dimension, ∆, a conserved particle number eigenvalue, N .”
Lectures on holographic methods for condensed matter physics (2009, background): “A modern field-theoretic discussion of the z = 2 Schrödinger algebra can be found in [34] .”
Hot spacetimes for cold atoms (2008, neutral): “July 2008”
Galilean Conformal Algebras and AdS/CFT (2009, background): “It was pointed out in [2] that the Schrodinger symmetry group [3, 4], a non-relativistic version of conformal symmetry, is relevant to the study of cold atoms.”
On Representations and Correlation Functions of Galilean Conformal Algebras (2009, background): “It was pointed out in [4] that the Schrödinger symmetry group [5, 6], a non-relativistic version of conformal symmetry, is relevant to the study of cold atoms.”
Holographic stress tensor for non-relativistic theories (2009, background): “Stronglycoupled theories with this scaling symmetry arise as critical points in condensed matter systems: two cases of interest are where the theory has a Galilean boost symmetry together with the anisotropic scaling symmetry, forming the Schrödinger symmetry group for z = 2 [10, 11, 12], and where ”
On string theory duals of Lifshitz-like fixed points (2009, background): “5 Gravity duals of another types of fixed points with non-relativistic scaling symmetry [15] have also been studied especially for systems with non-relativistic conformal invariance [16, 17, 18, 19, 20, 21].”
Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrodinger symmetry (2008, background): “(9) It has also been established that each primary operator corresponds to a eigenstate of the Hamiltonian of unitarity fermion in an isotropic harmonic potential of frequency ω [20, 23, 24].”
Non-relativistic holography (2008, background): “graphic duals to Galilean conformal field theories [ 1 ], and a number of subsequent papers”
Heating up Galilean holography (2008, background): “The reduction of the metric is straightforward, and gives (2.1) in five dimensions.”
Comments on string theory backgrounds with non-relativistic conformal symmetry (2008, background): “In particular, it is simple to see that the bulk viscosity coefficient vanishes, as dictated by conformal invariance [7, 47], and the shear viscosity has its universal value [48, 49].”