2015/10/26 by Siqi He, He, Siqi
Mathematics · Physics and Astronomy · #51P05 #70S15 #81T13 #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #hep-th #math.CA #math.DG #math.GT #msc:51P05 #msc:70S15 #msc:81T13
paper · pdf · doi:10.48550/arxiv.1510.07706
22 pages, 4 figures, in the 3rd version add the relation of the solutions and the Nahm Pole boundary condition
arxiv created 2016/03/13 · arxiv updated 2016/03/15
In the present paper, we find a system of non-linear ODEs that gives rotationally invariant solutions to the Kapustin-Witten equations in 4-dimensional Euclidean space. We explicitly solve these ODEs in some special cases and find decaying rational solutions, which provide solutions to the Kapustin-Witten equations. The imaginary parts of the solutions are singular. By rescaling, we find some limit behavior for these singular solutions. In addition, for any integer k, we can construct a 5|k| dimensional family of C1 solutions to the Kapustin-Witten equations on Euclidean space, again with singular imaginary parts. Moreover, we find solutions to the Kapustin-Witten equations over S3× (0,+∞) with the Nahm pole boundary condition.