Wilson Loops, Geometric Transitions and Bubbling Calabi-Yau's

Details Wilson Loops, Geometric Transitions and Bubbling Calabi-Yau's Wilson Loops, Geometric Transitions and Bubbling Calabi-Yau's

2006-12-19

arxiv.org/abs/hep-th/0612190v3

JHEP 0702:083,2007

Physics

High Energy Physics

High Energy Physics - Theory

26 pages; v.2 typos corrected, explanations clarified; v.3 typos corrected, reference added

Scientific paper

10.1088/1126-6708/2007/02/083

Motivated by recent developments in the AdS/CFT correspondence, we provide several alternative bulk descriptions of an arbitrary Wilson loop operator in Chern-Simons theory. Wilson loop operators in Chern-Simons theory can be given a description in terms of a configuration of branes or alternatively anti-branes in the resolved conifold geometry. The representation of the Wilson loop is encoded in the holonomy of the gauge field living on the dual brane configuration. By letting the branes undergo a new type of geometric transition, we argue that each Wilson loop operator can also be described by a bubbling Calabi-Yau geometry, whose topology encodes the representation of the Wilson loop. These Calabi-Yau manifolds provide a novel representation of knot invariants. For the unknot we confirm these identifications to all orders in the genus expansion.

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