Deformation quantizations from vertex operator algebras

Yiwen Pan, Wolfger Peelaers
2020 Journal of High Energy Physics  
In this note we address the question whether one can recover from the vertex operator algebra associated with a four-dimensional N = 2 superconformal field theory the deformation quantization of the Higgs branch of vacua that appears as a protected subsector in the three-dimensional circle-reduced theory. We answer this question positively if the UV R-symmetries do not mix with accidental (topological) symmetries along the renormalization group flow from the four-dimensional theory on a circle
more » ... o the threedimensional theory. If they do mix, we still find a deformation quantization but at different values of its period. 1 This SCFT/VOA correspondence has resulted in a large number of interesting results. For example, many SCFT/VOA pairs have been identified in, e.g., [2] [3] [4] [5] [6] [7] [8] , and, more remarkably, the correspondence has inspired the construction of novel vertex operator algebras [9] [10] [11] [12] [13] . It has also served as a useful tool to acquire new insights in SCFTs and VOAs, see for example [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] . 2 Also six-dimensional N = (2, 0) SCFTs participate in a truncation to vertex operator algebras [33] . 3 A similar construction exists for the Coulomb branch of vacua.
doi:10.1007/jhep06(2020)127 fatcat:u5krtlpg4rd6xg4g6hb3tiqqiq