3,326 research outputs found
Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions
Theories defined in higher than four dimensions have been used in various
frameworks and have a long and interesting history. Here we review certain
attempts, developed over the last years, towards the construction of unified
particle physics models in the context of higher-dimensional gauge theories
with non-commutative extra dimensions. These ideas have been developed in two
complementary ways, namely (i) starting with a higher-dimensional gauge theory
and dimensionally reducing it to four dimensions over fuzzy internal spaces and
(ii) starting with a four-dimensional, renormalizable gauge theory and
dynamically generating fuzzy extra dimensions. We describe the above approaches
and moreover we discuss the inclusion of fermions and the construction of
realistic chiral theories in this context
Localization for Yang-Mills Theory on the Fuzzy Sphere
We present a new model for Yang-Mills theory on the fuzzy sphere in which the
configuration space of gauge fields is given by a coadjoint orbit. In the
classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find
all classical solutions of the gauge theory and use nonabelian localization
techniques to write the partition function entirely as a sum over local
contributions from critical points of the action, which are evaluated
explicitly. The partition function of ordinary Yang-Mills theory on the sphere
is recovered in the classical limit as a sum over instantons. We also apply
abelian localization techniques and the geometry of symmetric spaces to derive
an explicit combinatorial expression for the partition function, and compare
the two approaches. These extend the standard techniques for solving gauge
theory on the sphere to the fuzzy case in a rigorous framework.Comment: 55 pages. V2: references added; V3: minor corrections, reference
added; Final version to be published in Communications in Mathematical
Physic
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