Complete solution of 2D superfield supergravity from graded Poisson-sigma models, and the super point particle

Abstract

Recently an alternative description of 2d supergravities in terms of graded Poisson-Sigma models (gPSM) has been given. As pointed out previously by the present authors a certain subset of gPSMs can be interpreted as "genuine" supergravity, fulfilling the well-known limits of supergravity, albeit deformed by the dilaton field. In our present paper we show that precisely that class of gPSMs corresponds one-to-one to the known dilaton supergravity superfield theories presented a long time ago by Park and Strominger. Therefore, the unique advantages of the gPSM approach can be exploited for the latter: We are able to provide the first complete classical solution for any such theory. On the other hand, the straightforward superfield formulation of the point particle in a supergravity background can be translated back into the gPSM frame, where "supergeodesics" can be discussed in terms of a minimal set of supergravity field degrees of freedom. Further possible applications like the (almost) trivial quantization are mentioned.

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

“…Note that the dilaton is denoted by φ in the appendices and not by X for sake of backward compatibility with the literature on dilaton SUGRA. With the prepotential (2.15) the explicit expressions for the Poisson tensor are [19]:…”

“…The action is determined by a function F(S) with S being a scalar superfield that has A as its lowest component (cf. [23], we adopt the notation of [19]). The two theories are equivalent with the identification…”

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

“…82 As in FOG there exists at least one Casimir function, which receives additional fermionic contributions:…”

“…For purely bosonic states this implies DetP αβ = 8Y − u 2 = 0 and thus C = 0. Furthermore, an additional fermionic Casimir function exists and it can be checked 35,82 that the quantitỹ…”

“…35,68,82 The bosonic line element again may be written in the form (1.9). From this result the extremality of BPS Killing horizons 84,85 is immediate since by virtue of the constraint (1.33) the conformally invariant potential acquires the form w(φ) = −e Q u 2 /8.…”