11,732 research outputs found
Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories
We explore the consequences of conformal symmetry for the operator product
expansions in nonrelativistic field theories. Similar to the relativistic case,
the OPE coefficients of descendants are related to that of the primary.
However, unlike relativistic CFTs the 3-point function of primaries is not
completely specified by conformal symmetry. Here, we show that the 3-point
function between operators with nonzero particle number, where (at least) one
operator has the lowest dimension allowed by unitarity, is determined up to a
numerical coefficient. We also look at the structure of the family tree of
primaries with zero particle number and discuss the presence of conservation
laws in this sector.Comment: 11 pages, 1 figure. V2 added reference
Nonrelativistic conformal field theories
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.Comment: 26 pages, 9 figures; added a comment on the convergence of epsilon
expansion
The Euler current and relativistic parity odd transport
For a spacetime of odd dimensions endowed with a unit vector field, we
introduce a new topological current that is identically conserved and whose
charge is equal to the Euler character of the even dimensional spacelike
foliations. The existence of this current allows us to introduce new
Chern-Simons-type terms in the effective field theories describing relativistic
quantum Hall states and (2+1) dimensional superfluids. Using effective field
theory, we calculate various correlation functions and identify transport
coefficients. In the quantum Hall case, this current provides the natural
relativistic generalization of the Wen-Zee term, required to characterize the
shift and Hall viscosity in quantum Hall systems. For the superfluid case this
term is required to have nonzero Hall viscosity and to describe superfluids
with non s-wave pairing.Comment: 24 pages. v2: added citations, corrected minor typos in appendi
Short-distance and short-time structure of a unitary Fermi gas
We consider the operator product expansions for unitarity fermions. We
compute the dynamic structure factor S(q,w) at large frequency and wavenumber
away from the one-particle peak. The overall normalization of S(q,w) is
determined by Tan's contact parameter, and the dependence on q and w is
obtained in closed analytic form. We also find energy deposited into the system
by small, rapid variations of the inverse scattering length.Comment: 11 pages, 8 figure
Coulomb impurity in graphene
We consider the problem of screening of an electrically charged impurity in a
clean graphene sheet. When electron-electron interactions are neglected, the
screening charge has a sign opposite to that of the impurity, and is localized
near the impurity. Interactions between electrons smear out the induced charge
density to give a large-distance tail that follows approximately, but not
exactly, an r^{-2} behavior and with a sign which is the same as that of the
impurity.Comment: 10 pages, 3 figures; (v2) Corrected sign error in Eq. (13); (v3)
corrected figure
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