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Fluxbrane Inflation

Arthur Hebecker, Sebastian C. Kraus, Dieter Lust, Stephan Steinfurt, Timo Weigand

TL;DR

This paper introduces fluxbrane inflation in genuine F-theory settings, where the inflaton is the relative position of two 7-branes and their non-supersymmetric flux induces a flat D-term potential in the large-volume regime, allowing inflation without warping. The authors compute the inflaton potential using both 10d supergravity and open-string one-loop methods on toroidal backgrounds, and generalize the results to Calabi–Yau manifolds, where inflation ends via tachyon condensation and brane recombination in a hybrid D-term framework. A key phenomenological insight is that the D7/D7 setup can naturally suppress cosmic strings (via $ frac12 extint_ extSigma F^2=0$), enabling compatibility with CMB constraints while maintaining a viable field range and e-foldings; they provide a quantitative analysis of the scalar potential, slow-roll parameters, and the COBE normalization. The work highlights crucial issues of moduli stabilization and possible $F$-term contributions, outlining strategies (e.g., large-volume stabilisation) and open questions for embedding in explicit CY compactifications. Overall, the study offers a concrete path to realize inflation in F-theory with a controllable D-term potential and realistic phenomenology, setting the stage for explicit realizations and detailed moduli analyses.

Abstract

As a first step towards inflation in genuinely F-theoretic setups, we propose a scenario where the inflaton is the relative position of two 7-branes on holomorphic 4-cycles. Non-supersymmetric gauge flux induces an attractive inter-brane potential. The latter is sufficiently flat in the supergravity regime of large volume moduli. Thus, in contrast to brane-antibrane inflation, fluxbrane inflation does not require warping. We calculate the inflaton potential both in the supergravity approximation and via an open-string one-loop computation on toroidal backgrounds. This leads us to propose a generalisation to genuine Calabi-Yau manifolds. We also comment on competing F-term effects. The end of inflation is marked by the condensation of tachyonic recombination fields between the 7-branes, triggering the formation of a bound state described as a stable extension along the 7-brane divisor. Hence our model fits in the framework of hybrid D-term inflation. We work out the main phenomenological properties of our D-term inflaton potential. In particular, our scenario of D7/D7 inflation avoids the familiar observational constraints associated with cosmic strings.

Fluxbrane Inflation

TL;DR

This paper introduces fluxbrane inflation in genuine F-theory settings, where the inflaton is the relative position of two 7-branes and their non-supersymmetric flux induces a flat D-term potential in the large-volume regime, allowing inflation without warping. The authors compute the inflaton potential using both 10d supergravity and open-string one-loop methods on toroidal backgrounds, and generalize the results to Calabi–Yau manifolds, where inflation ends via tachyon condensation and brane recombination in a hybrid D-term framework. A key phenomenological insight is that the D7/D7 setup can naturally suppress cosmic strings (via ), enabling compatibility with CMB constraints while maintaining a viable field range and e-foldings; they provide a quantitative analysis of the scalar potential, slow-roll parameters, and the COBE normalization. The work highlights crucial issues of moduli stabilization and possible -term contributions, outlining strategies (e.g., large-volume stabilisation) and open questions for embedding in explicit CY compactifications. Overall, the study offers a concrete path to realize inflation in F-theory with a controllable D-term potential and realistic phenomenology, setting the stage for explicit realizations and detailed moduli analyses.

Abstract

As a first step towards inflation in genuinely F-theoretic setups, we propose a scenario where the inflaton is the relative position of two 7-branes on holomorphic 4-cycles. Non-supersymmetric gauge flux induces an attractive inter-brane potential. The latter is sufficiently flat in the supergravity regime of large volume moduli. Thus, in contrast to brane-antibrane inflation, fluxbrane inflation does not require warping. We calculate the inflaton potential both in the supergravity approximation and via an open-string one-loop computation on toroidal backgrounds. This leads us to propose a generalisation to genuine Calabi-Yau manifolds. We also comment on competing F-term effects. The end of inflation is marked by the condensation of tachyonic recombination fields between the 7-branes, triggering the formation of a bound state described as a stable extension along the 7-brane divisor. Hence our model fits in the framework of hybrid D-term inflation. We work out the main phenomenological properties of our D-term inflaton potential. In particular, our scenario of D7/D7 inflation avoids the familiar observational constraints associated with cosmic strings.

Paper Structure

This paper contains 17 sections, 137 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The geometric Calabi-Yau setup for 7-brane hybrid inflation
  3. The general mechanism
  4. Constraints on generic Calabi-Yau backgrounds
  5. Fluxed D7/D7-brane potential on $T^6$
  6. Potential from 10d supergravity perspective
  7. Potential via one-loop string computation
  8. The brane potential on generic Calabi-Yau manifolds
  9. Phenomenological analysis
  10. Conclusions and outlook on moduli stabilisation and $F$-terms
  11. Supergravity computation of D7/D7 potential
  12. Derivation of supergravity solution for a magnetised D7-brane
  13. (Anti-)Self-dual flux decomposition
  14. Evaluating the one-loop integral
  15. Modular functions
  16. ...and 2 more sections

Figures (3)

  • Figure 1: Deforming homologous 7-branes on a Calabi-Yau.
  • Figure 2: Magnetised 7-branes on ${T}^2_1 \times {T}^2_2 \times {T}^2_3$.
  • Figure 3: Asymptotic behaviour of the left-hand side of (\ref{['integrand']}) for $\phi_{ab} = 0.1$. The graph shows the full expression (solid) as well as the approximations for $0\ll t\ll 1/\phi_{ab}$ (dashed) and for $t\gg 1/\phi_{ab}$ (dotted).