911 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
Hall viscosity, spin density, and torsion
We investigate the relationship between Hall viscosity, spin density and
response to geometric torsion. For the most general effective action for
relativistic gapped systems, the presence of non-universal terms implies that
there is no relationship between torsion response and Hall viscosity. We also
consider free relativistic and non-relativistic microscopic actions and again
verify the existence of analogous non-universal couplings. Explicit examples
demonstrate that torsion response is unrelated to both Hall viscosity and spin
density. We also argue that relativistic gapped theories must have vanishing
Hall viscosity in Lorentz invariant vacuums.Comment: 15 pages, 1 figur
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
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