A repository for computing U(1) Euclidean wormhole solutions for axion fields coupled to gravity. The calculations are related to the companion paper 2009.03917 (The Axion Quality Problem: Global Symmetry Breaking and Wormholes).
There are 4 main files in this repository for solving the following two cases:
- U(1) wormholes within Einstein Gravity
- u1.m: this contains the solver functions and implementation for solving the relevant equations in the companion paper (Eqs. (14) - (16))
- run-u1.nb: this notebook calls the functions in u1.m and sets up the global variable, it then solves for the boundary conditions at infinity and plots the results.
- U(1) wormholes within the axion-dilaton system in String Theory
- dilaton.m: similar to the u1.m file this contains the implementation for the axion-dilaton system (Eqs. (35) - (38))
- run-dilaton.nb: this runs the functions in dilaton.m and plots the results for the dilaton, radial field and metric function
Note: a very similar scheme can be written to solve the U(1) x U(1) case, but the initial condition solver is less automatic than in the U(1) case where a simple bisection method is efficient. As such, we do not include it in the illustrative examples given here.