A Q-manifold is a graded manifold endowed with a vector field of degree one squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of ``gauge fields'' (sections in the category of graded manifolds) and each cohomology class of a certain sub…
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7 results for “Q-bundles”
The paper extends a mathematical procedure for gauge theories and applies it to supersymmetric models.
problem Understanding gauge theories and their supersymmetric extensions.
method Multigraded generalizations of the AKSZ procedure and -bundles.
result Comparison of different approaches to supersymmetric sigma models.
Develops equivariant connections for Yang-Mills equations, simplifying interactions modeling.
problem Simplifying interactions modeling in Yang-Mills equations for different bundles.
method Introduces -equivariance to reduce Yang-Mills equations.
result Models electroweak interaction and interactions with differential and wave equations.
We study the Lagrangian antifield BRST formalism, formulated in terms of exterior horizontal forms on the infinite order jet space of graded fields for topological field theories associated to -bundles. In the case of a trivial Q-bundle with a flat fiber and arbitrary base, we prove that the BRST cohomology are isom…
New Q-manifolds theory integrates Lie algebroids.
problem Integrating Lie algebroids over smooth manifolds.
method Introducing Q-groupoids and Q-bundles, proving Lie algebroids arise from Q-manifolds.
result Transitive Lie algebroids over second countable, smooth manifolds are integrated to locally trivial Q-groupoids.
A nonassociative generalization of the principal fiber bundles with a smooth loop mapping on the fiber is presented. Our approach allows us to construct a new kind of gauge theories that involve higher ''nonassociative'' symmetries.
Develops a new approach to describe gauge theories with background fields using presymplectic structures.
problem Describing gauge theories with background fields using presymplectic structures.
method Extension of the presymplectic BV-AKSZ approach to include background fields.
result Gauge theories with background fields correspond to presymplectic gauge PDEs over gauge PDEs describing background fields.