Generalized Toda theory from six dimensions and the conifold

• Main Authors: Sam van Leuven, Gerben Oling
• Format: Article
• Language: English
• Published: SpringerOpen 2017-12-01
• Series: Journal of High Energy Physics
• Subjects: Conformal and W Symmetry; M-Theory; Supersymmetric Gauge Theory; Supersymmetry and Duality
• Online Access: http://link.springer.com/article/10.1007/JHEP12(2017)050

Abstract Recently, a physical derivation of the Alday-Gaiotto-Tachikawa correspondence has been put forward. A crucial role is played by the complex Chern-Simons theory arising in the 3d-3d correspondence, whose boundary modes lead to Toda theory on a Riemann surface. We explore several features of this derivation and subsequently argue that it can be extended to a generalization of the AGT correspondence. The latter involves codimension two defects in six dimensions that wrap the Riemann surface. We use a purely geometrical description of these defects and find that the generalized AGT setup can be modeled in a pole region using generalized conifolds. Furthermore, we argue that the ordinary conifold clarifies several features of the derivation of the original AGT correspondence.