Thraxions in String Theory

• Thraxions are ultralight axions arising in Type IIB Calabi–Yau flux compactifications with warped Klebanov–Strassler throats, characterized by integration of the RR two-form over local 2-cycles.
• Their masses are highly suppressed by the infrared warp factor (m_c ∝ w_IR^3 M_P), making them significantly lighter than conventional Kaluza–Klein modes or moduli.
• Integrated into effective supergravity frameworks, thraxions influence moduli stabilization and serve as promising candidates for fuzzy dark matter in string axiverse scenarios.

Thraxions are a class of ultralight axions arising in type IIB Calabi–Yau flux compactifications, specifically associated with strongly warped Klebanov–Strassler (KS) throat geometries at conifold transitions. Distinguished from axions tied to harmonic cycles, thraxions correspond to massive, nearly massless modes of the Ramond–Ramond two-form $C_2$, supported on 2-cycles that are trivial in the global homology but locally nontrivial at the tips of multi-throat structures. The mass of the thraxion is parametrically suppressed by the warp factor of the throat, making them much lighter than ordinary Kaluza–Klein or complex-structure moduli, with implications for dark matter phenomenology and string axiverse scenarios (Hebecker et al., 2018, Carta et al., 2021, Cicoli et al., 2021).

1. Geometric and Physical Origin

Thraxions originate in Type IIB compactifications on Calabi–Yau threefolds near points in complex-structure moduli space where $n$ three-cycles $A^i$ degenerate subject to $m$ homology relations $\sum_i p_i^I [A^i]=0$. Fluxes on the dual $B$-cycles produce multiple KS warped throats. In the simplest configuration (the “double-throat,” $n=2,\,m=1$), two KS throats share a family of $S^2$s which collapse at each throat tip; this $S^2$ is trivial in the full CY but nontrivial in each throat individually (Hebecker et al., 2018).

The four-dimensional thraxion field $c(x)$ is defined by integrating the RR two-form over the $n$0:

$n$1

This field is globally massive as the $n$2 is the boundary of a three-chain $n$3 in the manifold, breaking the putative shift symmetry. Locally, $n$4 appears as a Wilson line and exhibits nontrivial physics tied to the IR structure of the throats.

2. Mass Generation and Potential Structure

The thraxion mass arises due to flux backreaction and is highly suppressed by the warp factor $n$5 at the IR tip of the throat. The physical mass scaling is:

$n$6

In detail, the leading contributions are:

• Flux misalignment: A finite $n$7 excursion induces $n$8 units of $n$9-flux in the throats, generating local phases in the deformation parameters $A^i$0.
• Bulk constraint: The Calabi–Yau bulk enforces relations between the phases, introducing a potential $A^i$1.
• Kinetic suppression: The kinetic term is dominated in the UV and suppressed only logarithmically by warping. Consequently, the axion mass squared is suppressed by the cube of the warp factor:

$A^i$2

In multi-throat setups ($A^i$3), no-scale breaking effects lift the suppression, leading to $A^i$4 (Hebecker et al., 2018, Carta et al., 2021).

3. Moduli Stabilization and Effective Supergravity

The complete moduli stabilization including thraxions can be realized in both KKLT and Large Volume Scenario (LVS) setups:

• Kähler and complex-structure moduli are stabilized jointly with thraxions.
• The effective Kähler potential and superpotential contain explicit thraxion dependence:

$A^i$5

• Minimization of the supergravity scalar potential gives critical points in both $A^i$6 (Kähler) and $A^i$7 (thraxion) directions.
• In the double-throat case, the mass-squared exhibits six-fold warp suppression; with more than two throats and cross-couplings, only three-fold suppression remains (Carta et al., 2021).

4. Backreaction, Monodromy, and Potential Shape

Thraxion dynamics include significant backreaction effects:

• Angular-mode backreaction: Exciting the thraxion rotates the throat's $A^i$8 angle, leading to a finite monodromy. Shift $A^i$9 advances only to the next discrete supersymmetric vacuum, enlarging but not making the periodicity infinite (Hebecker et al., 2018).
• Potential flattening: The naive quadratic potential $m$0 is flattened to a (cosine) $m$1 due to angular-mode adjustments and energy costs associated with continuity along the radial direction.
• Drifting monodromies: In multi-throat systems, the effective superpotential can display interleaved harmonics, generating super-Planckian axion periodicities in the envelope but generically retaining sub-Planckian oscillatory structure.

These features have implications for axion inflation: the finite but enlarged periodicity and the oscillatory structure generically prevent realising large-field natural inflation, as the potential oscillates on sub-Planckian field distances (Hebecker et al., 2018).

5. String Model Building and Orientifold Statistics

The realization of thraxions depends on specific geometric and topological features in the compactification:

• Topological prerequisites: At least two independent shrinking (and exchanged) three-cycles are required; under a conifold transition these become resolution 2-cycles supporting the thraxion.
• CICY orientifold statistics: Out of $m$22 million CICY orientifolds, $m$3320,000 admit at least one “multi-thraxion transition.” The majority suffer from “frozen conifold” singularities where the conifold sits atop O7-planes, precluding deformation. A filtered database with explicit thraxion-friendly models (no frozen conifolds) is available (Carta et al., 2020, Carta et al., 2021).
• Multiplicity: Each multi-throat system generically holds a single thraxion. Larger multiplicities are possible but constrained by the geometric setup (Carta et al., 2021).

A summary table outlines the orientifold landscape:

Feature	Requisite for Thraxion	Statistic/Status
Shrinking 3-cycles	$m$4 (exchanged by involution)	$m$5320,000 CICY orientifolds admit transitions
Resolved-side axion cycle	2-cycles odd under involution	$m$6 required for survival
Frozen conifolds	Must be avoided	$m$790% of models have some; filtered set now available

6. Phenomenological Implications

Thraxions, having masses as low as $m$8–$m$9 eV and decay constants $\sum_i p_i^I [A^i]=0$0–$\sum_i p_i^I [A^i]=0$1 GeV, are robust candidates for fuzzy dark matter (FDM) in Large Volume Scenario compactifications. Their abundance from misalignment production matches the observed dark matter relic density for $\sum_i p_i^I [A^i]=0$2 initial angle under certain conditions and mild (sub-lattice) violations of the axionic Weak Gravity Conjecture (WGC) (Cicoli et al., 2021). In LVS, the expected parameter window for thraxion FDM is partly below current observational bounds but within reach of future surveys and pulsar timing arrays.

Benchmark values in LVS-type vacua:

Parameter	Value Range (LVS, $\sum_i p_i^I [A^i]=0$3)
$\sum_i p_i^I [A^i]=0$4	$\sum_i p_i^I [A^i]=0$5 – $\sum_i p_i^I [A^i]=0$6 eV
$\sum_i p_i^I [A^i]=0$7	$\sum_i p_i^I [A^i]=0$8 – $\sum_i p_i^I [A^i]=0$9 GeV
$B$0	$B$1 (for $B$2)

Common challenges include achieving a rigorous $B$3d EFT for warped throats, realising throat hierarchies in KKLT (requiring $B$4), and identifying orientifolds with suitable multi-throat motifs (Cicoli et al., 2021).

7. Constraints, WGC, and Model-Building Caveats

While thraxions provide new ultra-light axionic directions, several nontrivial constraints arise:

• Weak Gravity Conjecture: The leading nonperturbative instanton action $B$5 can exceed the naive axionic WGC, although the conjecture's sublattice version can hold due to heavier Euclidean D1-brane instantons (Hebecker et al., 2018, Cicoli et al., 2021).
• Scalar potential structure: In all known models, the long-wavelength periodicity enabling super-Planckian ranges is accompanied by unresolved sub-Planckian modulations.
• Global realizability: Construction of fully explicit global models is nontrivial due to frozen-conifold obstructions, though filtered datasets of CY orientifolds free from this pathology now exist (Carta et al., 2021, Carta et al., 2020).
• Astrophysical and cosmological bounds: Thraxion masses and decay constants can fall below current Lyman-α and isocurvature constraints but will be probed in future observations.

This body of research places thraxions at a distinctive intersection of string theory, axion physics, and dark matter, characterized by double (or triple) warping suppression, rich potential with monodromy and oscillatory structure, and controlled explicit realization in global Calabi–Yau orientifolds (Hebecker et al., 2018, Carta et al., 2021, Carta et al., 2020, Cicoli et al., 2021).