1. Chern-Simons theory with the exceptional gauge group as a refined topological string
- Author
-
Ruben L. Mkrtchyan
- Subjects
High Energy Physics - Theory ,Nuclear and High Energy Physics ,Vogel's universality ,Chern–Simons theory ,FOS: Physical sciences ,String theory ,Topology ,01 natural sciences ,High Energy Physics::Theory ,Gauge group ,0103 physical sciences ,C++ string handling ,010306 general physics ,E8 ,Mathematical Physics ,Physics ,Coupling constant ,Partition function (quantum field theory) ,010308 nuclear & particles physics ,Refined topological strings ,Mathematical Physics (math-ph) ,lcsh:QC1-999 ,High Energy Physics - Theory (hep-th) ,Chern-Simons theory ,Constant (mathematics) ,Exceptional gauge groups ,lcsh:Physics - Abstract
We present the partition function of Chern-Simons theory with the exceptional gauge group on three-sphere in the form of a partition function of the refined closed topological string with relation $2\tau=g_s(1-b) $ between single K\"ahler parameter $\tau$, string coupling constant $g_s$ and refinement parameter $b$, where $b=\frac{5}{3},\frac{5}{2},3,4,6$ for $G_2, F_4, E_6, E_7, E_8$, respectively. The non-zero BPS invariants $N^d_{J_L,J_R}$ ($d$ - degree) are $N^2_{0,\frac{1}{2}}=1, N^{11}_{0,1}=1$. Besides these terms, partition function of Chern-Simons theory contains term corresponding to the refined constant maps of string theory. Derivation is based on the universal (in Vogel's sense) form of a Chern-Simons partition function on three-sphere, restricted to exceptional line $Exc$ with Vogel's parameters satisfying $\gamma=2(\alpha+\beta)$. This line contains points, corresponding to the all exceptional groups. The same results are obtained for $F$ line $\gamma=\alpha+\beta$ (containing $SU(4), SO(10)$ and $E_6$ groups), with the non-zero $N^2_{0,\frac{1}{2}}=1, N^{7}_{0,1}=1$. In both cases refinement parameter $b$ ($=-\epsilon_2/\epsilon_1$ in terms of Nekrasov's parameters) is given in terms of universal parameters, restricted to the line, by $b=-\beta/\alpha$., Comment: 8 pages
- Published
- 2020
- Full Text
- View/download PDF