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Compactified 2HDM under the Non-SUSY AdS instability conjecture

M. A. Rbah, S. Saoud, R. Sammani, E. H. Saidi, R. Ahl Laamara

TL;DR

This work studies a compactified Two-Higgs-Doublet Model (2HDM) coupled to gravity on a circle, deriving a full three-dimensional effective action that includes tree-level Higgs terms, one-loop Kaluza-Klein corrections, and a Goldberger–Wise–inspired radion potential. By enforcing the non-supersymmetric AdS instability conjecture from the Swampland program, the authors find a model-independent lower bound on the heavy-Higgs mass, $M_H \gtrsim 680\,\mathrm{GeV}$, to avoid unstable AdS$_3$ vacua. The analysis demonstrates how extra-dimensional dynamics and quantum-gravity consistency conditions can yield sharp, testable predictions for extended Higgs sectors, linking radion stabilization and Higgs phenomenology to potential collider signatures around the 600–700 GeV range. Overall, the paper provides a controlled framework where Swampland-inspired constraints translate into concrete phenomenological bounds on the Higgs spectrum.

Abstract

We investigate how extra-dimensional dynamics influence the Higgs sector phenomenology by compactifying a Two-Higgs-Doublet Model (2HDM) coupled to 4D gravity on a circle $S^{1}$. The resulting effective potential includes tree-level 2HDM interactions, one-loop Coleman-Weinberg corrections from the Kaluza-Klein towers, and a radion contribution inspired by the Goldberger-Wise mechanism. We derive the full 3D effective action and show that, for the observed Higgs mass $m_{h}=125$ GeV, the radion potential admits a stable minimum, near-zero vacuum energy. By imposing the non-supersymmetric AdS instability conjecture as a quantum gravity consistency requirement, we obtain a model independent bound on the heavy Higgs sector, finding that the additional scalar states must satisfy $M_{H}\gtrsim 680$ GeV to avoid an unstable AdS$_{3}$ vacuum. Our results demonstrate how Swampland inspired constraints can yield sharp, phenomenologically testable predictions for extended Higgs sectors.

Compactified 2HDM under the Non-SUSY AdS instability conjecture

TL;DR

This work studies a compactified Two-Higgs-Doublet Model (2HDM) coupled to gravity on a circle, deriving a full three-dimensional effective action that includes tree-level Higgs terms, one-loop Kaluza-Klein corrections, and a Goldberger–Wise–inspired radion potential. By enforcing the non-supersymmetric AdS instability conjecture from the Swampland program, the authors find a model-independent lower bound on the heavy-Higgs mass, , to avoid unstable AdS vacua. The analysis demonstrates how extra-dimensional dynamics and quantum-gravity consistency conditions can yield sharp, testable predictions for extended Higgs sectors, linking radion stabilization and Higgs phenomenology to potential collider signatures around the 600–700 GeV range. Overall, the paper provides a controlled framework where Swampland-inspired constraints translate into concrete phenomenological bounds on the Higgs spectrum.

Abstract

We investigate how extra-dimensional dynamics influence the Higgs sector phenomenology by compactifying a Two-Higgs-Doublet Model (2HDM) coupled to 4D gravity on a circle . The resulting effective potential includes tree-level 2HDM interactions, one-loop Coleman-Weinberg corrections from the Kaluza-Klein towers, and a radion contribution inspired by the Goldberger-Wise mechanism. We derive the full 3D effective action and show that, for the observed Higgs mass GeV, the radion potential admits a stable minimum, near-zero vacuum energy. By imposing the non-supersymmetric AdS instability conjecture as a quantum gravity consistency requirement, we obtain a model independent bound on the heavy Higgs sector, finding that the additional scalar states must satisfy GeV to avoid an unstable AdS vacuum. Our results demonstrate how Swampland inspired constraints can yield sharp, phenomenologically testable predictions for extended Higgs sectors.

Paper Structure

This paper contains 10 sections, 22 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Model Setup
  3. The Two-Higgs-Doublet Model Framework
  4. Circle Compactification of the 2HDM+GR Action
  5. Effective potential from 2HDM Compactification
  6. One-Loop Structure of the 2HDM Scalar Potential
  7. Swampland constraints on Radion-induced Higgs phenomenology
  8. Radion induced phenomenology in the extended Higgs sector
  9. The non-SUSY AdS instability and implications for the 2HDM
  10. Discussion and Conclusion

Figures (4)

  • Figure 1: Effective potential $V_{\text{eff}}(R)$ for a light Higgs mass $M_h = 125\,\mathrm{GeV}$, evaluated at ${ \if@compatibility \mathchar"0116 {} \mathchar"0116 } = 240\,\mathrm{GeV}$. The minimum occurs at positive vacuum energy.
  • Figure 2: Effective potential $V_{\text{eff}}(R)$ for a heavy Higgs mass $M_H = 400\,\mathrm{GeV}$, evaluated at ${ \if@compatibility \mathchar"0116 {} \mathchar"0116 } = 340\,\mathrm{GeV}$. The minimum lies at negative vacuum energy.
  • Figure 3: Effective potential $V_{\text{eff}}(R)$ for light Higgs masses near the Standard Model value.
  • Figure 4: Effective potential $V_{\text{eff}}(R)$ for several heavy Higgs masses.