Cardy states as idempotents of fusion ring in string field theory

Isao Kishimoto, Yutaka Matsuo
2004 Physics Letters B  
With some assumptions, the algebra between Ishibashi states in string field theory can be reduced to a commutative ring. From this viewpoint, Cardy states can be identified with its idempotents. The algebra can be identified with a fusion ring for the rational conformal field theory and a group ring for the orbifold. This observation supports our previous observation that boundary states satisfy a universal idempotency relation under closed string star product.
doi:10.1016/j.physletb.2004.03.074 fatcat:mnp74j32nrbdxboqt42ysapvxe