Tri-vertices and SU(2)'s
arXiv:1012.2119 · doi:10.1007/JHEP02(2011)069
Abstract
We examine a class of N=2 supersymmetric gauge theories in (3+1) dimensions whose Lagrangians are determined by graphs consisting of two building blocks, namely a tri-vertex and a line. A line represents an SU(2) gauge group and a tri-vertex represents a matter field in the trifundamental representation of SU(2)^3. These graphs can be topologically classified by the genus and the number of external legs. This paper focuses on the hypermultiplet moduli spaces of the aforementioned theories. We compute the Hilbert series which count all chiral operators on the hypermultiplet moduli space. Several examples show that theories corresponding to different graphs with the same genus and the same number of external legs possess the same Hilbert series. This is in agreement with the conjecture that such theories are related to each other by S-duality. We also give a general expression for the Hilbert series for the graph with any genus and any number of external legs.
35 pages, 19 figures
References in corpus (5)
- Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
- S-duality in N=2 supersymmetric gauge theories
- Webs of five-branes and N=2 superconformal field theories
- Tinkertoys for Gaiotto Duality
- The gravity duals of N=2 superconformal field theories