Modular Invariance, Finiteness, and Misaligned Supersymmetry: New Constraints on the Numbers of Physical String States

TL;DR

This paper reveals that a hidden 'misaligned supersymmetry' in non-supersymmetric string theories ensures finiteness of amplitudes and constrains how supersymmetry can be broken without losing this property.

Contribution

It introduces the concept of misaligned supersymmetry as a fundamental mechanism ensuring string finiteness without full supersymmetry.

Findings

Misaligned supersymmetry is a universal feature in non-supersymmetric string spectra.

Misaligned supersymmetry guarantees the finiteness of string amplitudes.

Modular invariance constrains the distribution of physical states across all mass levels.

Abstract

We investigate the generic distribution of bosonic and fermionic states at all mass levels in non-supersymmetric string theories, and find that a hidden ``misaligned supersymmetry'' must always appear in the string spectrum. We show that this misaligned supersymmetry is ultimately responsible for the finiteness of string amplitudes in the absence of full spacetime supersymmetry, and therefore the existence of misaligned supersymmetry provides a natural constraint on the degree to which spacetime supersymmetry can be broken in string theory without destroying the finiteness of string amplitudes. Misaligned supersymmetry also explains how the requirements of modular invariance and absence of physical tachyons generically affect the distribution of states throughout the string spectrum, and implicitly furnishes a two-variable generalization of some well-known results in the theory of modular functions.