Surface Operator, Bubbling Calabi-Yau and AGT Relation

Abstract

Surface operators in N=2 four-dimensional gauge theories are interesting half-BPS objects. These operators inherit the connection of gauge theory with the Liouville conformal field theory, which was discovered by Alday, Gaiotto and Tachikawa. Moreover it has been proposed that toric branes in the A-model topological strings lead to surface operators via the geometric engineering. We analyze the surface operators by making good use of topological string theory. Starting from this point of view, we propose that the wave-function behavior of the topological open string amplitudes geometrically engineers the surface operator partition functions and the Gaiotto curves of corresponding gauge theories. We then study a peculiar feature that the surface operator corresponds to the insertion of the degenerate fields in the conformal field theory side. We show that this aspect can be realized as the geometric transition in topological string theory, and the insertion of a surface operator leads to the bubbling of the toric Calabi-Yau geometry.

36 pages, 14 figures. v2: minor changes and typos corrected

References in corpus (8)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Refined Topological Vertex
• On AGT relation in the case of U(3)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Asymptotically free N=2 theories and irregular conformal blocks
• Loop operators and S-duality from curves on Riemann surfaces
• D-branes as a Bubbling Calabi-Yau
• Phase space polarization and the topological string: a case study

Cited by in corpus (9)

• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Quantum Hitchin Systems via beta-deformed Matrix Models
• On W-algebras and the symmetries of defects of 6d N=(2,0) theory
• W(1+infinity) algebra as a symmetry behind AGT relation
• (de)Tails of Toda CFT
• Note on refined topological vertex, Jack polynomials and instanton counting