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Elementary Constituents Conjecture

Vinicius Nevoa, Sanjay Raman, Cumrun Vafa

TL;DR

The paper proposes the Elementary Constituents Conjecture (ECC), a dynamical strengthening of the Cobordism Conjecture in quantum gravity, arguing that bor domism generators can be trivialized by elementary defects whose tensions are sub-Planckian in some region of moduli space. Central to the construction is the attractor mechanism, which drives moduli toward core values that minimize intrinsic defect tension, ensuring $T\lesssim 1$ in Planck units. The authors substantiate the ECC with a wide array of supersymmetric and non-supersymmetric examples across M-theory, Type II D-branes, orientifolds, NHCs, S-folds, KO-theory defects, and torsion cycles in Calabi–Yau compactifications, showing consistent sub-Planckian tensions and ECC-consistent generator sets. They also discuss phenomenological applications, such as magnetic monopole constraints and potential-driven field-space trajectories, illustrating how the ECC interplays with other Swampland conjectures (WGC, Distance Conjecture) and may guide future searches for non-supersymmetric consistent backgrounds. Overall, the work argues that a regime exists in moduli space where bordism charges are carried by elementary, nearly tensionless constituents, and attractor dynamics ensure the system remains within this regime near defect cores, with broad implications for quantum gravity and beyond.

Abstract

In this note, we conjecture and provide evidence that quantum gravity cobordism classes are trivialized by elementary generators with tension at most order 1 in Planck units. Motivated by the attractor mechanism and a number of key examples, we propose that there is always a regime in the field space of the EFT in which the intrinsic tension of such an object is at most Planckian. This work brings together kinematic and dynamical aspects of cobordism defects in the context of the Swampland program.

Elementary Constituents Conjecture

TL;DR

The paper proposes the Elementary Constituents Conjecture (ECC), a dynamical strengthening of the Cobordism Conjecture in quantum gravity, arguing that bor domism generators can be trivialized by elementary defects whose tensions are sub-Planckian in some region of moduli space. Central to the construction is the attractor mechanism, which drives moduli toward core values that minimize intrinsic defect tension, ensuring in Planck units. The authors substantiate the ECC with a wide array of supersymmetric and non-supersymmetric examples across M-theory, Type II D-branes, orientifolds, NHCs, S-folds, KO-theory defects, and torsion cycles in Calabi–Yau compactifications, showing consistent sub-Planckian tensions and ECC-consistent generator sets. They also discuss phenomenological applications, such as magnetic monopole constraints and potential-driven field-space trajectories, illustrating how the ECC interplays with other Swampland conjectures (WGC, Distance Conjecture) and may guide future searches for non-supersymmetric consistent backgrounds. Overall, the work argues that a regime exists in moduli space where bordism charges are carried by elementary, nearly tensionless constituents, and attractor dynamics ensure the system remains within this regime near defect cores, with broad implications for quantum gravity and beyond.

Abstract

In this note, we conjecture and provide evidence that quantum gravity cobordism classes are trivialized by elementary generators with tension at most order 1 in Planck units. Motivated by the attractor mechanism and a number of key examples, we propose that there is always a regime in the field space of the EFT in which the intrinsic tension of such an object is at most Planckian. This work brings together kinematic and dynamical aspects of cobordism defects in the context of the Swampland program.

Paper Structure

This paper contains 43 sections, 89 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Topological Charges and Bordism
  3. Review of Cobordism Conjecture
  4. Gauged Symmetry and Bordism with Defects
  5. Topological Charges and Bordism
  6. Elementary Constituents Conjecture and Motivations
  7. The Conjecture
  8. Examples in M-theory
  9. Examples with Type II D-branes
  10. Attractor Mechanism
  11. Review of BPS Attractor Mechanism
  12. Generalized Attractor Mechanism
  13. Supersymmetric Examples
  14. Examples in Codimension Two
  15. Examples with Orientifolds
  16. ...and 28 more sections

Figures (2)

  • Figure 1: A schematic depiction of a junction defect forming a joint boundary for 24 NS5-branes as a trivialization of a K3 with 24 singularities sourcing $H_3$-flux. The red dots depict the singular nullbordism for $[S^3, H^3 = 1]$ around an NS5-brane, and the black dot represents the fourbrane which corresponds to a singular nullbordism for the entire singular K3 and is relative to the 24 NS5-branes.
  • Figure 2: An illustration of the heterotic zerobrane as a relative defect, trivializing the singular manifold consisting of $S^8$ equipped with a gauge bundle with nontrivial $\mathop{\mathrm{tr}}\nolimits_v F^4$ and an F1-string as a $H^7$-source.

Theorems & Definitions (1)

  • Conjecture 1: Elementary Constituents Conjecture