Quantization of 2D dilaton supergravity with matter

Abstract

General N = (1, 1) dilaton supergravity in two dimensions allows a background independent exact quantization of the geometric part, if these theories are formulated as specific graded Poisson-sigma models. The strategy developed for the bosonic case can be carried over, although considerable computational complications arise when the Hamiltonian constraints are evaluated in the presence of matter. Nevertheless, the constraint structure is the same as in the bosonic theory. In the matterless case gauge independent nonlocal correlators are calculated non-perturbatively. They respect local quantum triviality and allow a topological interpretation.In the presence of matter the ensuing nonlocal effective theory is expanded in matter loops. The lowest order tree vertices are derived and discussed, entailing the phenomenon of virtual black holes which essentially determine the corresponding Smatrix. Not all vertices are conformally invariant, but the S-matrix is invariant, as expected. Finally, the proper measure for the 1-loop corrections is addressed. It is argued how to exploit the results from fixed background quantization for our purposes.

Chemistry of Chern-Simons Supergravity: reduction to a BPS kink, oxidation to M-theory and thermodynamical aspects

“…However, dimensional reduction makes it natural to assume a non-trivial coupling of matter to the dilaton field. Though it has been shown recently that the basic properties of the quantization procedure in [41] are retained together with non-minimal coupling [42], this case has not yet been worked out in detail. Moreover, non-trivial couplings of the matter fields to the new scalar field Y could yield an even richer structure which will be worthwhile to study.…”

Boundary theories for dilaton supergravity in 2D

“…Thus, for instance, in view of the results obtained in [36,37], it would be interesting to explore whether it is possible to obtain a reparametrization theory from generalized models of dilaton (super)gravity [60]. Another interesting aspect to explore is related to non-perturbative local quantum triviality of bosonic [61] and supersymmetric [62] dilaton theories in 2D. The absence of any local quantum effects suggests that these theories are fully equivalent to some effective quantum theories at the boundary.…”

Wolfgang Kummer and the Vienna School of Dilaton (Super-)Gravity

“…Despite the complexity of these expressions it can be shown 47 that the secondary constraints with respect to the Dirac bracket obey an algebra of the type (1.20). In the case of minimal coupling, K(φ) = 1, the structure functions of the matterless theory (1.20) are reproduced, 53 while in the generic case additional matter contributions to the structure functions arise, explicit expression can be found in Ref. 47.…”