Refined Partition Functions for Open Superstrings with 4, 8 and 16 Supercharges

TL;DR

This paper analytically computes refined partition functions for the massive open string spectrum in superstring compactifications with 4, 8, and 16 supercharges, revealing universal state structures and asymptotic behaviors.

Contribution

It introduces a super-Poincare covariant method to compute refined partition functions for superstring spectra with various supercharges, highlighting universal states and their asymptotic properties.

Findings

Derived compact forms of partition functions for different supercharges

Analyzed asymptotic behaviors and Regge trajectories

Explicit large spin limit formula for four supercharges case

Abstract

We analyse the perturbative massive open string spectrum of even dimensional superstring compactifications with four, eight and sixteen supercharges. In each of such cases, we focus on universal states that exist independently on the internal geometry and other compatification details. We analytically compute refined partition functions that count these states at each mass level. Such refined partition functions are written in a super-Poincare covariant form, providing information on how supermultiplets transform under the little group and the R symmetry. Various asymptotic limits of the partition functions and their associated quantities, such as the leading and subleading Regge trajectories, are studied empirically and analytically. In the phenomenologically relevant case of four supercharges, the partition function can be cast into the most compact form and the asymptotic formula in the large spin limit is derived explicitly.