Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-10-07
Phys.Rev.D61:085005,2000
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 23 pages, 7 Postscript figures
Scientific paper
10.1103/PhysRevD.61.085005
We discuss topologically stable solitons in two-dimensional theories with the extended supersymmetry assuming that the spatial coordinate is compact. This problem arises in the consideration of the domain walls in the popular theories with compactified extra dimensions. Contrary to naive expectations, it is shown that the solitons on the cylinder can be BPS saturated. In the case of one chiral superfield, a complete theory of the BPS saturated solitons is worked out. We describe the classical solutions of the BPS equations. Depending on the choice of the Kahler metric, the number of such solutions can be arbitrarily large. Although the property of the BPS saturation is preserved order by order in perturbation theory, nonperturbative effects eliminate the majority of the classical BPS states upon passing to the quantum level. The number of the quantum BPS states is found. It is shown that the N=2 field theory includes an auxiliary N=1 quantum mechanics, Witten's index of which counts the number of the BPS particles.
Hou Xin-rui
Losev Andrei
Shifman Michael
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