Wheeler-DeWitt equation in Null-foliated spacetimes

TL;DR

This paper derives the Wheeler-DeWitt equation in null-foliated 4D spacetimes, revealing significant simplifications and a connection to string theory, with potential implications for understanding quantum gravity.

Contribution

It introduces a novel derivation of the Wheeler-DeWitt equation in null-foliated spacetimes and establishes a link to string worldsheet geometry.

Findings

Exact solutions for the Wheeler-DeWitt equation in null-foliated spacetimes

Identification of vertex operators of non-critical strings as solutions

Establishment of a correspondence between null surfaces and string worldsheet geometry

Abstract

In this paper, the Wheeler-DeWitt (WDW) equation is derived in null-foliated 4D spacetimes. WDW equation written in null-foliated spacetime presents an enormous simplification compared to the spacelike-foliated spacetime as the null-foliations are 2D. These can be solved exactly and uniquely to give the vertex operators of non-critical strings as a solution. A correspondence is established between null surfaces in 4D to string worldsheet geometry. Attempts are made to derive the physical consequences of this correspondence.