17,842 research outputs found
Groupoid Quantization of Loop Spaces
We review the various contexts in which quantized 2-plectic manifolds are
expected to appear within closed string theory and M-theory. We then discuss
how the quantization of a 2-plectic manifold can be reduced to ordinary
quantization of its loop space, which is a symplectic manifold. We demonstrate
how the latter can be quantized using groupoids. After reviewing the necessary
background, we present the groupoid quantization of the loop space of R^3 in
some detail.Comment: 19 pages, Proceedings of the Corfu Summer Institute 2011 - School and
Workshops on Elementary Particle Physics and Gravity, September 4-18, 2011,
Corfu, Greec
Branes, Quantization and Fuzzy Spheres
We propose generalized quantization axioms for Nambu-Poisson manifolds, which
allow for a geometric interpretation of n-Lie algebras and their enveloping
algebras. We illustrate these axioms by describing extensions of
Berezin-Toeplitz quantization to produce various examples of quantum spaces of
relevance to the dynamics of M-branes, such as fuzzy spheres in diverse
dimensions. We briefly describe preliminary steps towards making the notion of
quantized 2-plectic manifolds rigorous by extending the groupoid approach to
quantization of symplectic manifolds.Comment: 18 pages; Based on Review Talk at the Workshop on "Noncommutative
Field Theory and Gravity", Corfu Summer Institute on Elementary Particles and
Physics, September 8-12, 2010, Corfu, Greece; to be published in Proceedings
of Scienc
Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds
We describe the quantization of 2-plectic manifolds as they arise in the
context of the quantum geometry of M-branes and non-geometric flux
compactifications of closed string theory. We review the groupoid approach to
quantizing Poisson manifolds in detail, and then extend it to the loop spaces
of 2-plectic manifolds, which are naturally symplectic manifolds. In
particular, we discuss the groupoid quantization of the loop spaces of R^3, T^3
and S^3, and derive some interesting implications which match physical
expectations from string theory and M-theory.Comment: 71 pages, v2: references adde
Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation
We investigate masses of light mesons from a coupled system of
Dyson--Schwinger (DSE) and Bethe--Salpeter equations (BSE), taking into account
dominant non-Abelian, sub-leading Abelian, and dominant pion cloud
contributions to the dressed quark-gluon vertex. The axial-vector
Ward-Takahashi identity preserving Bethe-Salpeter kernel is constructed and the
spectrum of light mesons calculated. Our model goes significantly beyond the
rainbow-ladder. We find that sub-leading Abelian corrections are further
dynamically suppressed, and that our results supersede early qualitative
predictions from simple truncation schemes.Comment: 4 pages, 3 figures, 1 table. Talk given at the 5-th Int. Conf. on
Quarks and Nuclear Physics, Beijing, September 21-26,200
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