Notes on the dynamics of noncommutative U(2) and commutative SU(3) instantons

Smith, Douglas J.; Robson, Calum J.; Farrow, Joseph A.

Abstract

We examine the dynamics of noncommutative instantons of instanton number 2 and commutative instantons of instanton number 3 in 5D super Yang-Mills theory. We begin by detailing the construction of the 1=4-Bogamolyni-Prasad-Somerfeldt instanton solutions, their moduli space, and the moduli space potential using an explicit parametrization of the moduli space coordinates in terms of the biquaternions. We then go on to numerically analyze the dynamics on the moduli spaces we have constructed, discussing some of the numerical issues which arose, and describing the numerical algorithm we developed to solve them.

Citation

Smith, D. J., Robson, C. J., & Farrow, J. A. (2022). Notes on the dynamics of noncommutative U(2) and commutative SU(3) instantons. Physical Review D, 106(4), Article 045001. https://doi.org/10.1103/physrevd.106.045001

• Journal Article Type: Article
• Acceptance Date: Jun 9, 2022
• Online Publication Date: Aug 1, 2022
• Publication Date: 2022
• Deposit Date: Aug 8, 2022
• Publicly Available Date: Aug 8, 2022
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 106
• Issue: 4
• Article Number: 045001
• DOI: https://doi.org/10.1103/physrevd.106.045001