Refined topological vertex with ON-planes

Abstract

We propose refined topological vertex formalism for 5-brane systems with ON-planes by introducing a new vertex associated with reflection over an ON-plane, which gives rise to new vertex and edge factors. We test our proposal against various 5d $\mathcal{N}=1$ gauge theories which can be realized as 5-brane webs with ON-planes, which include $D$-type quiver theories. In particular, we compute the refined partition functions for 6d E-string theory on a circle as well as 5d SU(3) theory at the Chern-Simons level 9, which can be realized as 5-brane webs with two ON-planes. Our results completely agree with the known results.

v1: 49 pages, 20 figures; v2: published version

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Cited by in corpus (7)

• Quantum toroidal algebras and solvable structures in gauge/string theory
• Topological strings and Wilson loops
• ABCD of qq-characters
• Instantons on Young diagrams with matters
• $DE$-type little strings from glued brane webs
• O-vertex, O7${}^{+}$-plane, and Topological Vertex
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops