The Swampland Distance Conjecture and Towers of Tensionless Branes

TL;DR

The paper extends the Swampland Distance Conjecture to four-dimensional type II Calabi–Yau compactifications and shows that infinite-distance limits generate not only towers of light particles but also towers of tensionless domain walls and strings. Using IIA and IIB orientifolds, it analyzes how infinite Kähler, complex-structure, and dilaton directions produce these towers, with monodromy and nilpotent-orbit techniques organizing the spectra and leading to exponential suppression of tensions and masses with proper distance. The results are cross-checked with mirror symmetry, which requires incorporating exotic domain walls tied to non-geometric fluxes, and are illustrated in toroidal orbifolds where the relative scales of strings, branes, and KK modes are explicit. The findings have potential implications for emergence, the EFT cutoff, and the viability of moduli-stabilization scenarios, highlighting that towers of tensionless extended objects can influence low-energy physics in ways not captured by particle towers alone.

Abstract

The Swampland Distance Conjecture states that at infinite distance in the scalar moduli space an infinite tower of particles become exponentially massless. We study this issue in the context of 4d type IIA and type IIB Calabi-Yau compactifications. We find that for large moduli not only towers of particles but also domain walls and strings become tensionless. We study in detail the case of type IIA and IIB ${\cal N}=1$ CY orientifolds and show how for infinite Kähler and/or complex structure moduli towers of domain walls and strings become tensionless, depending on the particular direction in moduli space. For the type IIA case we construct the monodromy orbits of domain walls in detail. We study the structure of mass scales in these limits and find that these towers may occur at the same scale as the fundamental string scale or the KK scale making sometimes difficult an effective field theory description. The structure of IIA and IIB towers are consistent with mirror symmetry, as long as towers of exotic domain walls associated to non-geometric fluxes also appear. We briefly discuss the issue of emergence within this context and the possible implications for 4d vacua.

Figures (5)

• Figure 1: The monodromy maps some states into others with different mass and charge but the whole tower is mapped to itself.
• Figure 2: Energy scales associated to the 4d particles, strings and domain walls that become massless/tensionless and remain within the perturbative regime as we approach the infinite distance points given by (a) $s\propto u \propto t^{3/2} \rightarrow \infty$ and (b) $s\propto u \propto t^{3} \rightarrow \infty$. The string, KK and winding scales are also included. The subindices $P$, $S$ and $DW$ indicate whether the object is a particle, a string or a domain wall and the ones in blue and underlined are projected out by the orientifold action.
• Figure 3: Energy scales associated to the 4d particles, strings and domain walls that become massless/tensionless as we approach the infinite distance points given by (a) $t \rightarrow \infty, \ s, \ u$ fixed, (b) $u \rightarrow \infty,\ s \ \mathrm{ and }\ t$ fixed and (c) $s \propto u \rightarrow \infty, \ t$ fixed. The string, KK and winding scales are also included. The subindices $P$, $S$ and $DW$ indicate whether the object is a particle, a string or a domain wall and the ones in blue and underlined are projected out by the orientifold action.
• Figure 4: Spectra of towers of lightest particles and branes for different infinite limits in moduli space, for the $T^6/{\mathbb Z}_2 \times {\mathbb Z}_2^\prime$. The subindices $P$, $S$ and $DW$ indicate whether the object is a particle, a string or a domain wall and the underlined ones are projected out by the orientifold action.
• Figure 5: Energy scales associated to the 4d particles, strings and domain walls that become massless/tensionless at the infinite distance points given by (a) $u \rightarrow \infty$, $s$, $v$ fixed, (b) $v \rightarrow \infty$, $s$, $u$ fixed, and (c) $s \propto v \rightarrow \infty$, $u$ fixed. The string, KK and winding scales are also indicated. These are the T-duals of Fig. \ref{['fig:scalesuort']}. Objects in blue and underlined are projected out in the orientifold.