Spinor-Vector Duality and the Swampland

TL;DR

This paper explores the role of spinor-vector duality and other string theory symmetries, like mirror symmetry and T-duality, in constraining and understanding the structure of quantum gravity and the swampland.

Contribution

It introduces the concept of spinor-vector duality as an extension of mirror symmetry, proposing it as a tool to probe and constrain string compactification moduli spaces.

Findings

Spinor-vector duality extends mirror symmetry in string vacua.

String dualities impose significant constraints on effective field theories.

Phase-space duality and the equivalence postulate underpin quantum gravity theories.

Abstract

The Swampland Program aims to address the question, "when does an effective field theory model of quantum gravity have an ultraviolet complete embedding in string theory?", and can be regarded as a bottom-up approach to investigations of quantum gravity. An alternative top-down approach aim to explore the imprints and the constraints imposed by the string theory dualities and symmetries on the effective field theory representations of quantum gravity. The most celebrated example of this approach is mirror symmetry. Mirror symmetry was first observed in worldsheet contructions of string compactifications. It was completely unexpected from the effective field theory point of view, and its implications in that context were astounding. In terms of the moduli parameters of toroidally compactified Narain spaces, mirror symmetry can be regarded as arising from mappings of the moduli of the internal compactified space. Spinor-vector duality, which was discovered in worldsheet constructions of string vacua, is an extension of mirror symmetry that arises from mappings of the Wilson line moduli, and provide a probe to constrain and explore the moduli spaces of $(2,0)$ string compactifications. Mirror symmetry and spinor-vector duality are mere two examples of a much wider symmetry structure, whose implications are yet to be unravelled. A mapping between supersymmetric and non-supersymmetric vacua is briefly discussed. $T$-duality is another important property of string theory, and can be thought of as phase-space duality in compact space. I propose that manifest phase-space duality, and the related equivalence postulate of quantum mechanics, provide the background independent overarching principles underlying quantum gravity.