Supergravitons interacting with the super-Virasoro group

Short Distance Expansion from the Dual Representation of Infinite Dimensional Lie Algebras

“…The origin of this model independence is that we exploit the natural bifurcation of the initial data where the algebraic elements serve as conjugate momenta and the dual of the algebra serves as the conjugate coordinates. This feature is shared by the symplectic structures of actions like Yang-Mills theory and N -extended affirmative actions [16,4]. The coadjoint representation enforces a short distance expansion already at the level of the Poisson bracket of the elements with no Hamiltonian required.…”

“…One example of the distinction of these two types of actions for the SU(N) affine Lie algebra or what physicists sometimes call an SU(N) Kac-Moody algebra is its geometric action, an SU(N) WZNW model,and its transverse action, the two dimensional SU(N) Yang-Mills action. For the Virasoro algebra the geometric action is given by the two dimensional Polyakov action for gravity [26] and its corresponding transverse action given by the N = 0 affirmative action [16,4]. Besides these constructions, other areas of interests for the coadjoint representation are the BTZ black holes [2,3] that appear in the asymptotic Brown-Henneaux symmetry [7] on AdS 3 [36,24,2].…”

The diffeomorphism field

“…Just as in the ordinary case, the previously found superdiff action [19] corresponds to the symplectic part of this action :…”

“…We construct the transverse action for the diff field in Section 4.3. Its supersymmetric extension is obtained in Section 4.5 using [19] as a guide. We analyze the transverse diff theory in 2D Minkowski spacetime before covariantization in Section 6.2, and the covariantized theory in Sections 5.4 and 5.5.…”

“…Also we introduced D as the component multiplying θ so as to keep it bosonic. 5 The second equation here, is different from the equations in [19] and [28]. In each source the second equation was…”