Zero modes of the non-relativistic self-dual Chern-Simons vortices on the Toda backgrounds

✍ Scribed by Yongsung Yoon

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 698 KB
• Volume: 211
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(91)90208-p

✦ Synopsis

The two-dimensional self-dual equations are the governing equations of the static zeroenergy vortex solutions for the non-relativistic, non-Abelian Chern-Simons models. The zero modes of the non-relativistic vortices are examined by index calculation for the self-dual equations. The index for the self-dual equations is zero for non-Abelian groups, but a non-zero index is obtained by the Toda Ansarz which reduces the self-dual equations to the Toda equations. The number of zero modes for the non-relativistic Toda vortices is 2 XL,,{ K,,Q" which is twice the total number of isolated zeroes of the vortex functions. For the affme Toda system. there are additional adjoint zero modes which give a zero index for the SU(N) group.