Spinor-vector duality in 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 spinorvector 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.

Niemeier Lattices in the Free Fermionic Heterotic–String Formulation

“…In this section, we review the spinor-vector duality in the specific realisation of [27]. Construction of a consistent four-dimensional heterotic-string theory in the light-cone gauge requires 20 left-moving and 44 right-moving twodimensional real fermions [28,29] propagating on the world-sheet torus.…”

“…This is the four-dimensional manifestation of the twisted generation of gauge groups already observed in the ten-dimensional case. A few of the possibilities that may arise were classified in [27]. The same construction will be exploited in Section 3 in the analysis of compactifications to two dimensions.…”

Non-tachyonic semi-realistic non-supersymmetric heterotic-string vacua

“…This distinction affects the moduli spaces of the models [53], which can be entirely fixed in the former case [54] but not in the later. On the other hand the classification method enables the systematic scan of spaces of the order of 10 12 vacua, and led to the discovery of spinor-vector duality [46][47][48][55][56][57][58][59] and exophobic heterotic-string vacua [20,21]. In this paper, for reasons that will be clarified below, our discussion is focussed on the NAHE-based models.…”

LHC di-photon excess and gauge coupling unification in extra $$Z^\prime $$ Z ′ heterotic-string derived models

“…The model utilises the spinor-vector duality symmetry that was observed in the space of fermionic Z 2 × Z 2 orbifold compactifications [110][111][112][113][114]. The spinor-vector duality operates under exchange of the total number of spinorial (16⊕16) representations of SO (10) with the total number of vectorial 10 representations.…”

“…In Ref. [105] we used the spinor-vector duality property of Z 2 × Z 2 orbifolds [110][111][112][113][114] to construct a string derived model with anomaly free U (1) ζ , thus enabling it to remain unbroken down to low scales.…”