Some twisted self-dual solutions for the Yang-Mills equations on a hypertorus |
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Authors: | Gerard't Hooft |
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Institution: | (1) California Institute of Technology, 91125 Pasadena, CA, USA |
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Abstract: | TheSU(N) Yang-Mills equations are considered in a four-dimensional Euclidean box with periodic boundary conditions (hypertorus). Gauge-invariant twists can be introduced in these boundary conditions, to be labeled with integersn
![mgr](/content/hn65g02u04w46156/xxlarge956.gif)
(= –n
![mgr](/content/hn65g02u04w46156/xxlarge956.gif)
), defined moduloN. The Pontryagin number in this space is often fractional. Whenever this number is zero there are solutions to the equationsG
![mgr](/content/hn65g02u04w46156/xxlarge956.gif)
=0 HereG
![mgr](/content/hn65g02u04w46156/xxlarge956.gif)
is the covariant curl. When this number is not zero we find a set of solutions to the equations
, provided that the periodsa
of the box satisfy certain relations.Work supported in part by the US Department of Energy under Contract No. DE-AC-03-76ER 00068 and by the Fairchild FoundationOn leave from the Institute for Theoretical Physics, University of Utrecht, P.O. Box 80.006, NL-3508 TA Utrecht, The Netherlands |
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Keywords: | |
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