12 research outputs found
Topological entropy and renormalization group flow in 3-dimensional spherical spaces
We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit ß/a « 1 of a massive field theory in 3-dimensional spherical spaces, M 3, with constant curvature 6/a 2. For masses lower than 2p/ß , this term can be identified with the free energy of the same theory on M 3 considered as a 3-dimensional Euclidean space-time. The non-extensive part of this free energy, S hol, is generated by the holonomy of the spatial metric connection. We show that for homogeneous spherical spaces the holonomy entropy S hol decreases monotonically when the RG scale flows to the infrared. At the conformal fixed points the values of the holonomy entropy do coincide with the genuine topological entropies recently introduced. The monotonic behavior of the RG flow leads to an inequality between the topological entropies of the conformal field theories connected by such flow, i.e. S top UV¿>¿S top IR . From a 3-dimensional viewpoint the same term arises in the 3-dimensional Euclidean effective action and has the same monotonic behavior under the RG group flow. We conjecture that such monotonic behavior is generic, which would give rise to a 3-dimensional generalization of the c-theorem, along the lines of the 2-dimensional c-theorem and the 4-dimensional a-theorem. The conjecture is related to recent formulations of the F-theorem. In particular, the holonomy entropy on lens spaces is directly related to the topological Rényi entanglement entropy on disks of 2-dimensional flat spaces
On a spin conformal invariant on manifolds with boundary
On a n-dimensional connected compact manifold with non-empty boundary
equipped with a Riemannian metric, a spin structure and a chirality operator,
we study some properties of a spin conformal invariant defined from the first
eigenvalue of the Dirac operator under the chiral bag boundary condition. More
precisely, we show that we can derive a spinorial analogue of Aubin's
inequality.Comment: 26 page
Faraday rotation in graphene
We study magneto--optical properties of monolayer graphene by means of
quantum field theory methods in the framework of the Dirac model. We reveal a
good agreement between the Dirac model and a recent experiment on giant Faraday
rotation in cyclotron resonance. We also predict other regimes when the effects
are well pronounced. The general dependence of the Faraday rotation and
absorption on various parameters of samples is revealed both for suspended and
epitaxial graphene.Comment: 10 pp; v2: typos corrected and references added, v3, v4: small
changes and more reference
Energy Density of Vortices in the Schroedinger Picture
The one-loop energy density of an infinitely thin static magnetic vortex in
SU(2) Yang-Mills theory is evaluated using the Schroedinger picture. Both the
gluonic fluctuations as well as the quarks in the vortex background are
included. The energy density of the magnetic vortex is discussed as a function
of the magnetic flux. The center vortices correspond to local minima in the
effective potential. These minima are degenerated with the perturbative vacuum
if the fermions are ignored. Inclusion of fermions lifts this degeneracy,
raising the vortex energy above the energy of the perturbative vacuum.Comment: 25 pages, 2 figure
Massive 3+1 Aharonov-Bohm fermions in an MIT cylinder
We study the effect of a background flux string on the vacuum energy of
massive Dirac fermions in 3+1 dimensions confined to a finite spatial region
through MIT boundary conditions. We treat two admissible self-adjoint
extensions of the Hamiltonian. The external sector is also studied and
unambiguous results for the Casimir energy of massive fermions in the whole
space are obtained.Comment: 12 pages, 5 figures, LaTe
Fermionic current induced by magnetic flux in compactified cosmic string spacetime
In this paper, we investigate the fermionic current densities induced by a
magnetic flux running along the idealized cosmic string in a four-dimensional
spacetime, admitting that the coordinate along the string's axis is
compactified. In order to develop this investigation we construct the complete
set of fermionic mode functions obeying a general quasiperiodicity condition
along the compactified dimension. The vacuum expectation value of the azimuthal
current density is decomposed into two parts. The first one corresponds to the
uncompactified cosmic string geometry and the second one is the correction
induced by the compactification. For the first part we provide a closed
expression which includes various special cases previously discussed in the
literature. The second part is an odd periodic function of the magnetic flux
along the string axis with the period equal to the flux quantum and it is an
even function of the magnetic flux enclosed by the string axis. The
compactification of the cosmic string axis in combination with the
quasiperiodicity condition leads to the nonzero axial current density. The
latter is an even periodic function of the magnetic flux along the string axis
and an odd periodic function of the magnetic flux enclosed by the string axis.
The axial current density vanishes for untwisted and twisted fields in the
absence of the magnetic flux enclosed by the string axis. The asymptotic
behavior of the vacuum fermionic current is investigated near the string and at
large distances from it. In particular, the topological part of the azimuthal
current and the axial current are finite on the string's axis.Comment: 22 pages, 4 figure