18,031 research outputs found
Zero Field Hall Effect in (2+1)-dimensional QED
In QED of two space dimensions, a quantum Hall effect occurs in the absence
of any magnetic field. We give a simple and transparent explanation. In solid
state physics, the Hall conductivity for non-degenerate ground state is
expected to be given by an integer, the Chern number. In our field-free
situation, however, the conductivity is in natural units. We fit this
half-integral result into the topological setting and give a geometric
explanation reconciling the points of view of QFT and solid state physics. For
quasi-periodic boundary conditions, we calculate the finite size correction to
the Hall conductivity. Applications to graphene and similar materials are
discussed
About Twistor Spinors with Zero in Lorentzian Geometry
We describe the local conformal geometry of a Lorentzian spin manifold
admitting a twistor spinor with zero. Moreover, we describe the
shape of the zero set of . If has isolated zeros then the metric
is locally conformally equivalent to a static monopole. In the other case
the zero set consists of null geodesic(s) and is locally conformally
equivalent to a Brinkmann metric. Our arguments utilise tractor calculus in an
essential way. The Dirac current of , which is a conformal Killing vector
field, plays an important role for our discussion as well
An algebraic approach to minimal models in CFTs
CFTs are naturally defined on Riemann surfaces. The rational ones can be
solved using methods from algebraic geometry. One particular feature is the
covariance of the partition function under the mapping class group. In genus
, this yields modular forms, which can be linked to ordinary differential
equations of hypergeometric type with algebraic solutions.Comment: 30 pages. Revised and extended version. (The paper was originally
part of arXiv:1305.0469, which had been split into the present paper and
arXiv:1705.07627.
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