Interaction of the Virasoro and Kac-Moody Algebras Through Effective Actions

Salvatore Quaid

Abstract: The effective Polyakov action describes the conformal anomaly's contribution to gravity and arises naturally in string theory and two-dimensional general relativity. It can also be sourced directly as the geometric action from the Virasoro algebra, but now with a new field present that transforms in the coadjoint representation of the Virasoro algebra. Similarly, the Wess-Zumino-Witten action describes the chiral anomalys contribution to particle physics and directly leads to the observable decay of pi-zero to two photons. It can also be sourced directly as the geometric action from the Kac-Moody algebra, but now with a new field present that transforms in the coadjoint representation of the Kac-Moody algebra. By identifying the new field in the effective Polyakov action with the Diffeomorphism field of Thomas-Whitehead projective gravity, and that of the Wess-Zumino-Witten action with a gauge field, we can realize the interaction of the algebras as the fully dynamical form of the interaction of the conformal and chiral anomalies. The Dirac brackets and constraint analysis of this interaction is explored for this interaction. General solutions to Hamilton's equations of motion are found, and a quantum Hamiltonian is found. Application to the full constraint surface is explored, as are the cosmological ramifications of the interaction of the coadjoint element of the Virasoro algebra with that of the Kac-Moody algebra.

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