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

Abstract

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.

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

References in corpus (11)

• Holographic Wilson Loops
• Wilson Loops of Anti-symmetric Representation and D5-branes
• On gravitational description of Wilson lines
• Wilson Loops as D3-Branes
• Higher rank Wilson loops from a matrix model
• Wilson Loops in N=4 SYM and Fermion Droplets
• Multiply wound Polyakov loops at strong coupling
• Ghost D-branes
• Bubbling Defect CFT's
• Operator product expansion of higher rank Wilson loops from D-branes and matrix models
• Calibrated Surfaces and Supersymmetric Wilson Loops

Cited by in corpus (18)

• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• Bubbling Surface Operators And S-Duality
• Semi-classical open string corrections and symmetric Wilson loops
• D-branes as a Bubbling Calabi-Yau
• Topological Holography: The Example of The D2-D4 Brane System
• A prediction for bubbling geometries
• Bubbling Calabi-Yau geometry from matrix models
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Wilson Loops in 3d QFT from D-branes in AdS(4) x CP**3
• Entanglement entropy and edge modes in topological string theory II: The dual gauge theory story
• Two-Point Functions in ABJM Matrix Model
• Surface Operators from M-strings
• Topological string entanglement
• Geometric transition in Non-perturbative Topological string
• Wilson Loops from D-branes in AdS(4) X CP**3 with B-NS Holonomy
• D-brane Description of New Open String Solutions in AdS(5)
• BIons in topological string theory
• Near Horizon Geometry of Strings Ending on Intersecting D8/D4-branes