Grassmannian coset models and unitary representations of w

TLDR: In this paper, it was shown that the 2-d coset models SU(p + 1)N/SU(p)N ⊗ U(1) provide unitary representations of the chiral operator algebra W∞ in the large level (N → ∞) limit, with central charge c = 2p.

Abstract: It is shown that the 2 – d coset models SU(p + 1)N/SU(p)N ⊗ U(1) provide unitary representations of the chiral operator algebra W∞ in the large level (N → ∞) limit, with central charge c = 2p. For p ≥ 2, the corresponding field theories possess additional symmetries which given rise to a U(p) matrix generalization of W∞, denoted by $W_\infty^p$. Its commutation relations are obtained in closed form for all values of p and W∞ is identified with the U(1) trace part of $W_\infty^p$. It is also shown that $W_\infty^p$ at large p is associated with the algebra of symplectic diffeomorphisms in four dimensions.