Dirac Geometry of the Holonomy Fibration
Abstract
In this paper, we solve the problem of giving a gaugetheoretic description of the natural Dirac structure on a Lie Group which plays a prominent role in the theory of Dbranes for the WessZuminoWitten model as well as the theory of quasiHamiltonian spaces. We describe the structure as an infinitedimensional reduction of the space of connections over the circle. Our insight is that the formal Poisson structure on the space of connections is not an actual Poisson structure, but is itself a Dirac structure, due to the fact that it is defined by an unbounded operator. We also develop general tools for reducing Courant algebroids and morphisms between them, allowing us to give a precise correspondence between Hamiltonian loop group spaces and quasiHamiltonian spaces.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 November 2017
 DOI:
 10.1007/s0022001729364
 arXiv:
 arXiv:1508.06168
 Bibcode:
 2017CMaPh.355..865C
 Keywords:

 Mathematics  Symplectic Geometry;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 40 pages