Abstract
For each magic basis of Lie g, it is known that the Virasoro master equation on affine g contains a generalized graph theory of conformal level-families. In this paper, it is found that the superconformal master equation on affine g×SO(dim g) similarly contains a generalized graph theory of superconformal level-families for each magic basis of g. The superconformal level-families satisfy linear equations on the generalized graphs, and the first exact unitary irrational solutions of the superconformal master equation are obtained on the sine-area graphs of g=SU(n), including the simplest unitary irrational central charges c=6nx/(nx+8 sin2(rsπ/n)) yet observed in the program.
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