6d/5d exceptional gauge theories from web diagrams

Abstract

Abstract We construct novel web diagrams with a trivalent or quadrivalent gluing for various 6d/5d theories from certain Higgsings of 6d conformal matter theories on a circle. The theories realized on the web diagrams include 5d Kaluza-Klein theories from circle compactifications of the 6d G 2 gauge theory with 4 flavors, the 6d F 4 gauge theory with 3 flavors, the 6d E 6 gauge theory with 4 flavors and the 6d E 7 gauge theory with 3 flavors. The Higgsings also give rise to 5d Kaluza-Klein theories from twisted compactifications of 6d theories including the 5d pure SU(3) gauge theory with the Chern-Simons level 9 and the 5d pure SU(4) gauge theory with the Chern-Simons level 8. We also compute the Nekrasov partition functions of the theories by applying the topological vertex formalism to the newly obtained web diagrams.

Keywords

• Brane Dynamics in Gauge Theories
• Conformal Field Models in String Theory
• Field Theories in Higher Dimensions
• Topological Strings