Is there a problem with quantum wormhole states inN=1 supergravity?

Abstract

The issue concerning the existence of wormhole states in locally supersymmetric minisuperspace models with matter is addressed. Wormhole states are apparently absent in models obtained from the more general theory of N=1 supergravity with supermatter. A Hartle-Hawking type solution can be found, even though some terms (which are scalar field dependent) cannot be determined in a satisfactory way. A possible cause is investigated here. As far as the wormhole situation is concerned, we argue here that the type of Lagrange multipliers and fermionic derivative ordering used can make a difference. A proposal is made for supersymmetric quantum wormholes to also be invested with a Hilbert space structure, associated with a maximal analytical extension of the corresponding minisuperspace.

Conserved Currents in Supersymmetric Quantum Cosmology?

“…In particular, the no-boundary wave function has now been adequately identified, in contrast with previous comments in ref. [22]- [25], [28,29].…”

“…In the absence of matter the Hartle-Hawking state [33] is therefore given by Ψ HH = ψ A ψ A e 3σ 2 a 2 . The solution Ψ = e −3σ 2 a 2 bears quantum wormhole properties [16,17,28,29,34]. Furthermore, we get the expressions A = d 1 e −3σ 2 a 2 e c 1 (φ 1 −iφ 2 ) and E = d 2 e 3σ 2 a 2 e c 2 (φ 1 +iφ 2 ) from the decomposition φ = φ 1 + iφ 2 .…”

“…In section 2 we analyse a k = +1 FRW model in the framework of N=1 supergravity with a scalar supermultiplet [15]- [18], [22]- [25], [28]- [30]. Some improvements concerning the results present in [22]- [25], [28,29] are included. We also point to specific differences between our FRW model and the ones analysed in ref.…”

“…It seems unsatisfactory that we cannot obtain from the Lorentz and supersymmetry constraints the explicit dependence of Ψ on φ,φ (see ref. [15]- [17], [22]- [25], [28,29]). However, this apparent drawback can be circumvented as follows.…”

“…(19), (24) and ref. [15]- [17], [22]- [25], [28,29]. If we had use φ = φ 1 + iφ 2 then the corresponding first-order differential equations would lead to…”