DLCQ On a Twisted Torus

TL;DR

This paper investigates how the shape angle of a torus affects physics in DLCQ compactifications, finding that only specific angles are compatible and solutions remain consistent within those constraints.

Contribution

It demonstrates that in DLCQ, toroidal compactification is restricted to certain shape angles, ensuring numerical solutions are unaffected for those angles.

Findings

Toroidal compactification in DLCQ is limited to specific shape angles.

Numerical solutions are invariant for allowed shape angles.

Shape angle dependence is crucial in compactified models.

Abstract

Recently it has been demonstrated by Dienes and Mafi, that the physics of toroidal compactified models of extra dimensions can depend on the shape angle of the torus. Toroidal compactification has also recently been used as a regulator for numerical solutions of supersymmetric fields theories in 2+1 dimensions. The question is; does the shape angle of the torus also affect the physics in this situation? Clearly a numerical solution should be independent of the shape of the space we compactify on. We show that within the context of standard DLCQ, that toroidal compactification is only allowed for a specific set of shape angles and for that set of shape angles the numerical solutions are unchanged.