1996/12/27 by Carlos Castro, Castro, Carlos
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9612241
46 pages, tex file. Extended updated version of hep-th/9605029 and hep-th/9612160
arxiv created 1996/12/27 · arxiv updated 2009/11/30
The exact quantum integrability aspects of a sector of the membrane is investigated. It is found that spherical membranes moving in flat target spacetime backgrounds admit a class of integrable solutions linked to SU(infty) SDYM equations (dimensionally reduced to one temporal dimension). After a suitable ansatz, the SDYM equations can be recast in the form of the continuous Toda molecule equations whose symmetry algebra is the dimensional reduction of the W (infty plus W(infty algebra. The latter algebra is explicitly constructed. Highest weight representations are built directly from the infinite number of defining relations among the highest weight states of W(∞) algebras and the quantum states of the Toda molecule. Discrete states are also constructed. The full (dimensionaly reduced) quantum SU(infty) YM theory remains to be explored.