323,676 research outputs found

    C*-Algebras over Topological Spaces: The Bootstrap Class

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    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

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    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

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    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

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    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

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    We study the quantized topological terms in a weak-coupling gauge theory with gauge group GgG_g and a global symmetry GsG_s in dd space-time dimensions. We show that the quantized topological terms are classified by a pair (G,νd)(G,\nu_d), where GG is an extension of GsG_s by GgG_g and νd\nu_d an element in group cohomology \cH^d(G,\R/\Z). When d=3d=3 and/or when GgG_g 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 G/Gg=GsG/G_g=G_s. We also apply our theory to a simple case Gs=Gg=Z2G_s=G_g=Z_2, which leads to 12 different SET phases in 2+1D, where quasiparticles have different patterns of fractional Gs=Z2G_s=Z_2 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 GsG_s, which may lead to different fractionalizations of GsG_s 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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