4,290 research outputs found
Topological Order and the Quantum Spin Hall Effect
The quantum spin Hall (QSH) phase is a time reversal invariant electronic
state with a bulk electronic band gap that supports the transport of charge and
spin in gapless edge states. We show that this phase is associated with a novel
topological invariant, which distinguishes it from an ordinary insulator.
The classification, which is defined for time reversal invariant
Hamiltonians, is analogous to the Chern number classification of the quantum
Hall effect. We establish the order of the QSH phase in the two band
model of graphene and propose a generalization of the formalism applicable to
multi band and interacting systems.Comment: 4 pages RevTeX. Added reference, minor correction
Real secondary index theory
In this paper, we study the family index of a family of spin manifolds. In
particular, we discuss to which extend the real index (of the Dirac operator of
the real spinor bundle if the fiber dimension is divisible by 8) which can be
defined in this case contains extra information over the complex index (the
index of its complexification). We study this question under the additional
assumption that the complex index vanishes on the k-skeleton of B. In this
case, using local index theory we define new analytical invariants \hat c_k\in
H^{k-1}(B;\reals/\integers). We then continue and describe these invariants in
terms of known topological characteristic classes. Moreover, we show that it is
an interesting new non-trivial invariant in many examples.Comment: LaTeX2e, 56 pages; v2: final version to appear in ATG, typos fixed,
statement of 4.5.5 improve
D-branes in Orbifold Singularities and Equivariant K-Theory
The study of brane-antibrane configurations in string theory leads to the
understanding of supersymmetric D-branes as the bound states of higher
dimensional branes. Configurations of pairs brane-antibrane do admit in a
natural way their description in terms of K-theory. We analyze configurations
of brane-antibrane at fixed point orbifold singularities in terms of
equivariant K-theory as recently suggested by Witten. Type I and IIB fivebranes
and small instantons on ALE singularities are described in K-theoretic terms
and their relation to Kronheimer-Nakajima construction of instantons is also
provided. Finally the D-brane charge formula is reexamined in this context.Comment: 32 pages, harvmac file, no figures, version to appear in Nucl.Phys.
On Nahm's transformation with twisted boundary conditions
Following two different tracks, we arrive at a definition of Nahm's
transformation valid for self-dual fields on the 4-dimensional torus with
non-zero twist tensor.The transform is again a self-dual gauge field defined on
a new torus and with non-zero twist tensor. It preserves the property of being
an involution.Comment: 18 page
Twisted -theory
Twisted complex -theory can be defined for a space equipped with a
bundle of complex projective spaces, or, equivalently, with a bundle of
C-algebras. Up to equivalence, the twisting corresponds to an element of
. We give a systematic account of the definition and basic
properties of the twisted theory, emphasizing some points where it behaves
differently from ordinary -theory. (We omit, however, its relations to
classical cohomology, which we shall treat in a sequel.) We develop an
equivariant version of the theory for the action of a compact Lie group,
proving that then the twistings are classified by the equivariant cohomology
group . We also consider some basic examples of twisted -theory
classes, related to those appearing in the recent work of
Freed-Hopkins-Teleman.Comment: 49 pages;some minor corrections have been made to the earlier versio
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