A tour through N=2 strings

TL;DR

This paper reviews N=2 strings, deriving their effective field theories, analyzing one-loop amplitudes, and discussing inconsistencies and potential resolutions related to Lorentz invariance and supersymmetry.

Contribution

It provides a comprehensive overview of N=2 strings, including derivations of effective theories and analysis of loop amplitude inconsistencies and their possible resolutions.

Findings

One-loop amplitudes exhibit incurable infra-red divergences.

Discrepancies in spacetime dimension when comparing string amplitudes to effective theories.

Closed-string three-point amplitude can be expressed with a Schwinger parameter.

Abstract

I give an overview of open, closed and heterotic N=2 strings. At the tree level I derive the effective field theories of all the strings, and discuss the group theory of the N=2 open string and the interaction between its open and closed sectors. At one loop N=2 string loop amplitudes and partition functions have incurable infra-red divergences, and show puzzling disagreements on the dimension of spacetime when compared to their effective field theories. I show that the closed-string three-point amplitude can be written directly in terms of a Schwinger parameter, so explicitly exhibiting the inconsistency. I finally discuss the possibility that the puzzles posed by the loop amplitudes could be solved if the N=2 theories were Lorentz invariant and supersymmetric, and I speculate on possible modifications of the string calculations.