Spinor-Vector Duality in N=2 Heterotic String Vacua

TL;DR

This paper demonstrates the existence of a spinor-vector duality in N=2 heterotic string vacua, revealing a symmetry that interchanges spinorial and vectorial representations within the unbroken SO(12) GUT symmetry, supported by algebraic proof and a new basis for model generation.

Contribution

The paper extends the spinor-vector duality symmetry to N=2 heterotic string models and introduces a novel basis for generating free fermionic models that highlights this duality.

Findings

Confirmed spinor-vector duality in N=2 heterotic models.

Provided algebraic proof of the duality map.

Introduced a new basis emphasizing SO(8) triality.

Abstract

Classification of the N=1 space-time supersymmetric fermionic Z2XZ2 heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S_t <-> V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor--vector duality exists also in fermionic Z2 heterotic string models, which preserve N=2 space-time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S_t <-> V duality map. We present a novel basis to generate the free fermionic models in which the ten dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non--trivial sectors, and due to the triality property of the SO(8) representations. Thus, while in the new basis the appearance of GUT symmetries is more cumbersome, it may be more instrumental in revealing the duality symmetries that underly the string vacua.