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Journal of High Energy Physics

, 2019:38 | Cite as

The Universal Geometry of heterotic vacua

  • Philip CandelasEmail author
  • Xenia de la Ossa
  • Jock McOrist
  • Roberto Sisca
Open Access
Regular Article - Theoretical Physics
  • 8 Downloads

Abstract

We consider a family of perturbative heterotic string backgrounds. These are complex threefolds X with c1 = 0, each with a gauge field solving the Hermitian Yang-Mill’s equations and compatible B and H fields that satisfy the anomaly cancellation conditions. Our perspective is to consider a geometry in which these backgrounds are fibred over a parameter space. If the manifold X has coordinates x, and parameters are denoted by y, then it is natural to consider coordinate transformations \( x\to \tilde{x}\left(x,y\right)\kern0.5em \mathrm{and}\kern0.5em y\to \tilde{y}(y) \). Similarly, gauge transformations of the gauge field and B field also depend on both x and y. In the process of defining deformations of the background fields that are suitably covariant under these transformations, it turns out to be natural to extend the gauge field A to a gauge field \( \mathbb{A} \) on the extended (x, y)-space. Similarly, the B, H, and other fields are also extended. The total space of the fibration of the heterotic structures is the Universal Geometry of the title. The extension of gauge fields has been studied in relation to Donaldson theory and monopole moduli spaces. String vacua furnish a richer application of these ideas. One advantage of this point of view is that previously disparate results are unified into a simple tensor formulation. In a previous paper, by three of the present authors, the metric on the moduli space of heterotic theories was derived, correct through \( \mathcal{O} \)(α′), and it was shown how this was related to a simple Kähler potential. With the present formalism, we are able to rederive the results of this previously long and involved calculation, in less than a page.

Keywords

Superstring Vacua Superstrings and Heterotic Strings 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Philip Candelas
    • 1
    Email author
  • Xenia de la Ossa
    • 1
  • Jock McOrist
    • 2
  • Roberto Sisca
    • 2
  1. 1.Mathematical InstituteUniversity of OxfordOxfordU.K.
  2. 2.Department of MathematicsUniversity of SurreyGuildfordU.K.

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