5-brane webs for 5d N $$ \mathcal{N} $$ = 1 G 2 gauge theories
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Springer
Received: January 22, 2018 Accepted: March 15, 2018 Published: March 21, 2018
5-brane webs for 5d N = 1 G2 gauge theories
a
Department of Physics, School of Science, Tokai University, 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan b School of Physics, University of Electronic Science and Technology of China, North Jianshe Road, Chengdu 611731, China c Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China d School of Physics, Korea Institute for Advanced Study, 85 Hoegi-ro Dongdaemun-gu, Seoul 02455, Korea e Department of Physics, Technion — Israel Institute of Technology, Haifa 32000, Israel
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We propose 5-brane webs for 5d 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 f or an O5-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. Keywords: Brane Dynamics in Gauge Theories, Conformal Field Models in String Theory, Field Theories in Higher Dimensions ArXiv ePrint: 1801.03916
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP03(2018)125
JHEP03(2018)125
Hirotaka Hayashi,a Sung-Soo Kim,b,c Kimyeong Leed and Futoshi Yagie
Contents 1 Introduction f gauge theories from an O5-plane SO(7) gauge theory with spinor matter 5-brane web for pure G2 gauge theory Check from effective prepotential Adding flavors to G2
3 3 6 10 15
3 Another 5-brane web for pure G2 gauge theory 3.1 Higgsing 5d SO(8) gauge theory with one spinor and one conjugate spinor 3.2 Check from effective prepotential
16 16 19
4 5d Nekrasov partition functions of G2 gauge theories f 4.1 Vertex formalism with an O5- and O5-plane 4.2 Pure G2 gauge theory 4.3 G2 gauge theory with one flavor
21 21 23 27
5 Conclusion
31
1
Introduction
5-brane webs in type IIB string theory have been used to study five-dimensional (5d) superconformal field theories (SCFTs) that are ultraviolet (UV) completions of a certain class of 5d N = 1 supersymmetric gauge theories [1–6]. A 5-brane web configuration provides us with a tool to compute the instanton partition function that captures the BPS spectrum of a 5d theory realized on a 5-brane web as well as with a perspective of qualitative understandings of the SCFTs such as global symmetry enhancements and various dualities. By introducing an orientifold plane like an O7-plane or an O5-plane, 5-brane webs can be enriched so that one can describe 5d theories with some other classical gauge group, such as SO(N ), USp(2N ) [7–10], in addition to the standard classi
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