Anomalous transport on the lattice. Pavel Buividovich (Regensburg). Chiral Magnetic Effect [ Kharzeev , Warringa , Fukushima]. Chiral Separation Effect [Son, Zhitnitsky ]. Chiral Vortical Effect [ Erdmenger et al. , Banerjee et al. ]. Anomalous transport: CME, CSE, CVE.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
ρ = 1.0, m = 0.05
ρ = 1.4, m = 0.01
ρ = 1.4, m = 0.05
Bulk definition of μ5 !!! Around 20% deviation
is NOT a small perturbation
“triangle diagram” argument invalid
(Flux is quantized, 0 → 1 is not a perturbation, just like an instanton number)
More advanced argument:
in a finite volume
Solution: hide extra flux in the delta-function
Fermions don’t note this singularity if
Now go to the Landau-level basis:
Higher Landau levels
Chirality n5 is (in principle) observable
Express everything in terms of n5
To linear order in μ5:
Singularities of Π33cancel !!!
Note: no non-renormalization for two loops or higher and no dimensional reduction due to 4D gluons!!!
Relation to canonical formalism
Virtual photon hits out fermions
out of Fermi sphere…
(not chiral, but simple and works well)
gauge transformations of Aμ(x)
Linear equations for “projected” overlap or
Dirac operator with chiral chemical potential
Consistent currents!Naturaldefinition:charge transfer
Numerically impossible for arbitrary background…
Krylov subspace methods? Work in progress…
Derivatives of GW/inverse GW projection:
Good agreement with continuum expression
Small momenta/large size: continuum result
At small momenta, agreement with PV regularization
As lattice size increases, PV result is approached
Replace Dov with projected operator
Lüscher transformations Usual chiral rotations
Agreement with PV, but large artifacts
They might be crucial in interacting theories
[M. Knechtet al., hep-ph/0311100]
How the situation can be improved, probably?
Momentum from shifted BC [H.Meyer, 1011.2727]
We can get total conserved momentum
First Lx,Ly→∞ at fixed Lz, Lt, Φ !!!
Six equations for four unknowns… Solution:
Full phase space is available only at |p|>2|kF|