Exotica and discreteness in the classification of string spectra

TL;DR

This paper explores discrete symmetries and properties in the classification of free fermionic heterotic-string vacua, revealing patterns like spinor-vector duality and constraints on certain GUT models through algebraic and computational analysis.

Contribution

It introduces algebraic expressions for GSO projections enabling comprehensive computerised analysis of string vacua and uncovers new discrete symmetries and constraints in various GUT models.

Findings

Discovery of spinor-vector duality at the SO(10) level

Existence of exophobic Pati-Salam vacua

No exophobic Flipped SU(5) vacua with an odd number of generations

Abstract

I discuss the existence of discrete properties in the landscape of free fermionic heterotic-string vacua that were discovered via their classification by SO(10) GUT models and its subgroups such as the Pati-Salam, Flipped SU(5) and SU(4) x SU(2) x U(1) models. The classification is carried out by fixing a set of basis vectors and varying the GGSO projection coefficients entering the one-loop partition function. The analysis of the models is facilitated by deriving algebraic expressions for the GSO projections that enable a computerised analysis of the entire string spectrum and the scanning of large spaces of vacua. The analysis reveals discrete symmetries like the spinor-vector duality observed at the SO(10) level and the existence of exophobic Pati-Salam vacua. Contrary to the Pati-Salam case the classification shows that there are no exophobic Flipped SU(5) vacua with an odd number of generations. It is observed that the SU(4) x SU(2) x U(1) models are substantially more constrained.