# A dynamical metric and its ground state from the breaking down of the topological invariance of the Euler characteristic

## TL;DR

This paper constructs exact quantum wave functionals for a graviton-like field theory derived from breaking topological invariance, providing insights into its ground state and symmetry properties.

## Contribution

It introduces a new class of wave functionals for a modified string-inspired field theory, exploring their properties and potential as ground states.

## Key findings

- Wave functionals are explicitly constructed for the theory.
- Comparison suggests these functionals approximate the ground state.
- Symmetry analysis reveals continuous and discrete invariances.

## Abstract

Quantum state wave functionals are constructed in exact form for the graviton-like field theory obtained by breaking down the topological symmetry of the string action related with the Euler characteristic of the world-surface; their continuous and discrete symmetries are discussed. The comparison with the so-called Chern-Simons state, which may be inappropriate as quantum state, allows us to conclude that the found wave functionals will give a plausible approximation to the ground state for the considered field theory.