Worldsheet CFTs for Flat Monodrofolds

TL;DR

This paper constructs consistent worldsheet CFTs for strings in flat spacetimes with nontrivial Wilson lines, resolving a level mismatch puzzle and demonstrating physical consistency in various examples, including T-folds with fixed moduli.

Contribution

It introduces a novel quantization scheme for twisted sectors in string backgrounds with Wilson lines, ensuring consistency and physical principles are satisfied.

Findings

Resolved level mismatch in twisted sectors by adjusting momentum quantization.

Constructed a new 7D N=1 SUSY solution with fixed moduli for T-folds.

Demonstrated enhanced gauge symmetry and self-T-duality at small base size.

Abstract

We resolve a puzzle in the theory of strings propagating on locally flat spacetimes with nontrivial Wilson lines for stringy Z_N gauge symmetries. We find that strings probing such backgrounds are described by consistent worldsheet CFTs. The level mismatch in the twisted sectors is compensated by adjusting the quantization of momentum of strings winding around the Wilson line direction in units of 1/(N^2 R) rather than 1/(N R), as might have been classically expected. We demonstrate in various examples how this improvement of the naive orbifold prescription leads to satisfaction of general physical principles such as level matching and closure of the OPE. Applying our techniques to construct a Wilson line for T-duality of a torus in the type II string (``T-fold''), we find a new 7D solution with N=1 SUSY where the moduli of the fiber torus are fixed. When the size of the base becomes small this simple monodrofold exhibits enhanced gauge symmetry and a self-T-duality on the S^1 base.