Spinor-vector duality in [formula omitted] heterotic string vacua

Abstract

Classification of the N = 1 space–time supersymmetric fermionic Z 2 × Z 2 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 Z 2 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.