2000/07/31 by Chen-Gang Zhou, Zhou, Chen-Gang
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0007255
Harvmac, 16 pages, 2 figures
arxiv created 2000/07/31 · arxiv updated 2009/11/30
We investigate the behavior of the noncommutative scalar soliton solutions at finite noncommutative scale θ. A detailed analysis of the equation of the motion indicates that fewer and fewer soliton solutions exist as θ is decreased and thus the solitonic sector of the theory exhibits an overall hierarchy structure. If the potential is bounded below, there is a finite θc below which all the solitons cease to exist even though the noncommutativity is still present. If the potential is not bounded below, for any nonzero θ there is always a soliton solution, which becomes singular only at θ= 0. The ϕ4 potential is studied in detail and it is found the critical (θm2)c =13.92 (m2 is the coefficient of the quadratic term in the potential) is universal for all the symmetric ϕ4 potential.