Refined topological vertex with ON-planes
Sung-Soo Kim, Xing-Yue Wei

TL;DR
This paper introduces a refined topological vertex formalism for 5-brane systems with ON-planes, enabling precise computation of partition functions for complex gauge theories, and confirms its validity through agreement with known results.
Contribution
It develops a new refined topological vertex formalism incorporating ON-planes, expanding computational tools for 5-brane web theories and related gauge theories.
Findings
Successfully computes partition functions for 6d E-string theory on a circle.
Accurately calculates 5d SU(3) theory partition function at Chern-Simons level 9.
Results match known theoretical predictions, validating the new formalism.
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 gauge theories which can be realized as 5-brane webs with ON-planes, which include -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.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
