Center-vortex solutions of the Yang-Mills effective action in three and four dimensions

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 66, Issue 9, 2002, Pages

  Maul, Martin ^b  

^a NORDITA   (Denmark)

^b LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; ENERGY TRANSFER; MOLECULAR DYNAMICS; QUANTUM MECHANICS; THEORY; VACUUM; VORTEX MOTION;

EID: 0036870772     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.66.096004     Document Type: Article

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6. The only possible loophole in this analysis, known as “Derick’s theorem,” is if the field strength of the vortex is allowed to decrease weakly (as (Formula presented) at large transverse distances. Then the variation of the energy functional with size could have a full-divergence piece which potentially could destroy the argument. [This is what happens in the case of 3D Bogomol’nyi-Prasad-Sommerfield (BPS) monopoles.] Such behavior, however, would lead to the divergent transverse energy. Thus the conclusion that there are no vortex-type solutions of the YM classical equations holds true. In a compactified space the situation is different. In Ref. 7 a vortexlike classical solution has been obtained numerically in a partially compactified (Formula presented) space with the torus circumference much less than the size of the (Formula presented) box. In this case the scale is set by the compactification circumference. The radius of the vortex has been found to be of the order of the (short) length in the compact direction 7.
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