The Case of the Missing Wormhole State

TL;DR

This paper investigates the absence of wormhole states in supersymmetric minisuperspace models with matter, exploring how different formulations and operator orderings affect their existence and proposing a Hilbert space framework for quantum wormholes.

Contribution

It analyzes the conditions under which supersymmetric quantum wormholes can exist and suggests a Hilbert space structure for these solutions, addressing previous ambiguities.

Findings

Wormhole states are absent in certain supergravity models.

Operator ordering and Lagrange multiplier choices influence wormhole solutions.

A Hilbert space framework for supersymmetric quantum wormholes is proposed.

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 one uses may 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.