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RR photons

Pablo G. Camara, Luis E. Ibañez, Fernando Marchesano

TL;DR

This paper investigates how Ramond–Ramond $U(1)$ gauge bosons in Type II string compactifications can mix with the Standard Model hypercharge, either kinetically or via Stückelberg mass terms, with a focus on Type IIA orientifolds and their M-theory lifts. It develops a geometric framework to describe open–closed string $U(1)$ mixing, including the role of torsional cycles which produce discrete gauge symmetries and Aharonov–Bohm effects, and provides explicit examples (e.g., Enriques Calabi–Yau) to illustrate these mechanisms. A key finding is that mass mixing can occur through torsion, leading to massless gauge bosons that are linear combinations of D6-brane and RR $U(1)$s, and that such mixings can have phenomenological consequences, such as corrections to hypercharge gauge coupling unification in F-theory GUTs. The work thus connects RR sectors, torsion in the internal manifold, and open-string sectors within a unified M-theory/F-theory perspective, offering new avenues for observable signatures and gauge coupling considerations in string-inspired models.

Abstract

Type II string compactifications to 4d generically contain massless Ramond-Ramond U(1) gauge symmetries. However there is no massless matter charged under these U(1)'s, which makes a priori difficult to measure any physical consequences of their existence. There is however a window of opportunity if these RR U(1)'s mix with the hypercharge $U(1)_Y$ (hence with the photon). In this paper we study in detail different avenues by which $U(1)_{RR}$ bosons may mix with D-brane U(1)'s. We concentrate on Type IIA orientifolds and their M-theory lift, and provide geometric criteria for the existence of such mixing, which may occur either via standard kinetic mixing or via the mass terms induced by Stückelberg couplings. The latter case is particularly interesting, and appears whenever D-branes wrap torsional $p$-cycles in the compactification manifold. We also show that in the presence of torsional cycles discrete gauge symmetries and Aharanov-Bohm strings and particles appear in the 4d effective action, and that type IIA Stückelberg couplings can be understood in terms of torsional (co)homology in M-theory. We provide examples of Type IIA Calabi-Yau orientifolds in which the required torsional cycles exist and kinetic mixing induced by mass mixing is present. We discuss some phenomenological consequences of our findings. In particular, we find that mass mixing may induce corrections relevant for hypercharge gauge coupling unification in F-theory SU(5) GUT's.

RR photons

TL;DR

This paper investigates how Ramond–Ramond gauge bosons in Type II string compactifications can mix with the Standard Model hypercharge, either kinetically or via Stückelberg mass terms, with a focus on Type IIA orientifolds and their M-theory lifts. It develops a geometric framework to describe open–closed string mixing, including the role of torsional cycles which produce discrete gauge symmetries and Aharonov–Bohm effects, and provides explicit examples (e.g., Enriques Calabi–Yau) to illustrate these mechanisms. A key finding is that mass mixing can occur through torsion, leading to massless gauge bosons that are linear combinations of D6-brane and RR s, and that such mixings can have phenomenological consequences, such as corrections to hypercharge gauge coupling unification in F-theory GUTs. The work thus connects RR sectors, torsion in the internal manifold, and open-string sectors within a unified M-theory/F-theory perspective, offering new avenues for observable signatures and gauge coupling considerations in string-inspired models.

Abstract

Type II string compactifications to 4d generically contain massless Ramond-Ramond U(1) gauge symmetries. However there is no massless matter charged under these U(1)'s, which makes a priori difficult to measure any physical consequences of their existence. There is however a window of opportunity if these RR U(1)'s mix with the hypercharge (hence with the photon). In this paper we study in detail different avenues by which bosons may mix with D-brane U(1)'s. We concentrate on Type IIA orientifolds and their M-theory lift, and provide geometric criteria for the existence of such mixing, which may occur either via standard kinetic mixing or via the mass terms induced by Stückelberg couplings. The latter case is particularly interesting, and appears whenever D-branes wrap torsional -cycles in the compactification manifold. We also show that in the presence of torsional cycles discrete gauge symmetries and Aharanov-Bohm strings and particles appear in the 4d effective action, and that type IIA Stückelberg couplings can be understood in terms of torsional (co)homology in M-theory. We provide examples of Type IIA Calabi-Yau orientifolds in which the required torsional cycles exist and kinetic mixing induced by mass mixing is present. We discuss some phenomenological consequences of our findings. In particular, we find that mass mixing may induce corrections relevant for hypercharge gauge coupling unification in F-theory SU(5) GUT's.

Paper Structure

This paper contains 21 sections, 168 equations, 2 figures, 7 tables.

Table of Contents

  1. Introduction
  2. U(1)'s in type IIA compactifications
  3. Type IIA orientifold compactifications
  4. Open string U(1)'s
  5. Closed string U(1)'s
  6. Lift to M-theory
  7. Kinetic mixing with RR photons
  8. Mass mixing with RR photons
  9. Torsion and discrete gauge symmetries
  10. Massive RR U(1)'s from torsion
  11. The Stückelberg mechanism revisited
  12. M-theory and discrete gauge symmetries
  13. An explicit example
  14. Some phenomenological implications
  15. Adding background fluxes
  16. ...and 6 more sections

Figures (2)

  • Figure 1: Configuration of 4 fractional D6-branes leading to two mutually hidden sectors which communicate via RR photons.
  • Figure 2: Two-loop running of the MSSM gauge coupling constants in the region around $10^{16}$ GeV Ibe:2003ys. The shaded region represents the uncertainty in the measurement of the QCD gauge coupling constant.