Abstract
We propose 5-brane webs for 5d mathcal{N} = 1 G2 gauge theories. From a Higgsing of the SO(7) gauge theory with a hypermultiplet in the spinor representation, we construct two types of 5-brane web configurations for the pure G2 gauge theory using an O5-plane or an tilde{mathrm{O}5} -plane. Adding flavors to the 5-brane web for the pure G2 gauge theory is also discussed. Based on the obtained 5-brane webs, we compute the partition functions for the 5d G2 gauge theories using the recently suggested topological vertex formulation with an O5-plane, and we find agreement with known results.
Highlights
We propose 5-brane webs for 5d N = 1 G2 gauge theories
The purpose of this paper is to further extend the study of 5-brane webs with an O5plane and propose 5-brane web diagrams for 5d N = 1 gauge theories of an exceptional gauge group G2, using these recent developments on 5-brane webs
We studied 5d N = 1 G2 gauge theories from 5-brane web diagrams with an O5-plane in type IIB string theory
Summary
A wide class of 5d theories with eight supercharges can be constructed by (p, q) 5-brane webs in type IIB string theory [5, 6, 20] or M-theory on Calabi-Yau threefolds [2,3,4]. The web diagram for the pure SO(7) gauge theory can be derived by a Higgsing of the SO(8) gauge theory with a hypermultiplet in the vector representation Through this process, we will see that the O5-plane is accompanied by the half monodromy cut. The 5-brane web diagram after moving the half D7-branes in the opposite directions is given in figure 2 This is exactly the web diagram for the pure SO(7) gauge theory, which have three color D5-branes with the O5 -plane. After considering the transition in figure 7 for the local USp(0) part, the 5-brane web diagram becomes the one in figure 9(a) We obtain another 5-brane web diagram given in figure 9(a) which realizes the SO(7) gauge theory with one spinor. The D5-brane on the O5-plane disappears and we have an O5-plane realized with the half monodromy cut
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