323,676 research outputs found
C*-Algebras over Topological Spaces: The Bootstrap Class
We carefully define and study C*-algebras over topological spaces, possibly
non-Hausdorff, and review some relevant results from point-set topology along
the way. We explain the triangulated category structure on the bivariant
Kasparov theory over a topological space. We introduce and describe an analogue
of the bootstrap class for C*-algebras over a finite topological space.Comment: Final version, very minor change
Topological Vector Symmetry of BRSTQFT and Construction of Maximal Supersymmetry
The scalar and vector topological Yang-Mills symmetries determine a closed
and consistent sector of Yang-Mills supersymmetry. We provide a geometrical
construction of these symmetries, based on a horizontality condition on
reducible manifolds. This yields globally well-defined scalar and vector
topological BRST operators. These operators generate a subalgebra of maximally
supersymmetric Yang-Mills theory, which is small enough to be closed off-shell
with a finite set of auxiliary fields and large enough to determine the
Yang-Mills supersymmetric theory. Poincar\'e supersymmetry is reached in the
limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs
is thus removed by the requirement of scalar and vector topological symmetry,
which also determines the complete supersymmetry transformations in a twisted
way. Provided additional Killing vectors exist on the manifold, an equivariant
extension of our geometrical framework is provided, and the resulting
"equivariant topological field theory" corresponds to the twist of super
Yang-Mills theory on Omega backgrounds.Comment: 50 page
Topological Interpretation of Barbero-Immirzi Parameter
We set up a canonical Hamiltonian formulation for a theory of gravity based
on a Lagrangian density made up of the Hilbert-Palatini term and, instead of
the Holst term, the Nieh-Yan topological density. The resulting set of
constraints in the time gauge are shown to lead to a theory in terms of a real
SU(2) connection which is exactly the same as that of Barbero and Immirzi with
the coefficient of the Nieh-Yan term identified as the inverse of
Barbero-Immirzi parameter. This provides a topological interpretation for this
parameter. Matter coupling can then be introduced in the usual manner, {\em
without} changing the universal topological Nieh-Yan term.Comment: 14 pages, revtex4, no figures. Minor modifications with additional
remarks. References rearrange
SU(2) gauge theory of gravity with topological invariants
The most general gravity Lagrangian in four dimensions contains three
topological densities, namely Nieh-Yan, Pontryagin and Euler, in addition to
the Hilbert-Palatini term. We set up a Hamiltonian formulation based on this
Lagrangian. The resulting canonical theory depends on three parameters which
are coefficients of these terms and is shown to admit a real SU(2) gauge
theoretic interpretation with a set of seven first-class constraints. Thus, in
addition to the Newton's constant, the theory of gravity contains three
(topological) coupling constants, which might have non-trivial imports in the
quantum theory.Comment: Based on a talk at Loops-11, Madrid, Spain; To appear in Journal of
Physics: Conference Serie
Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
We study the quantized topological terms in a weak-coupling gauge theory with
gauge group and a global symmetry in space-time dimensions. We
show that the quantized topological terms are classified by a pair ,
where is an extension of by and an element in group
cohomology \cH^d(G,\R/\Z). When and/or when is finite, the
weak-coupling gauge theories with quantized topological terms describe gapped
symmetry enriched topological (SET) phases (i.e. gapped long-range entangled
phases with symmetry). Thus, those SET phases are classified by
\cH^d(G,\R/\Z), where . We also apply our theory to a simple case
, which leads to 12 different SET phases in 2+1D, where
quasiparticles have different patterns of fractional quantum numbers
and fractional statistics. If the weak-coupling gauge theories are gapless,
then the different quantized topological terms may describe different gapless
phases of the gauge theories with a symmetry , which may lead to different
fractionalizations of quantum numbers and different fractional statistics
(if in 2+1D).Comment: 13 pages, 2 figures, PRB accepted version with added clarification on
obtaining G_s charge for a given PSG with non-trivial topological terms.
arXiv admin note: text overlap with arXiv:1301.767
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