Dynamical Tadpoles, Stringy Cobordism, and the SM from Spontaneous Compactification

TL;DR

This work shows that dynamical tadpoles in string vacua enforce a finite spacetime extent, Δ, controlled by the tadpole strength via Δ^{-n} ∼ 𝒯, and that the resulting ends of spacetime are cobordism defects predicted by the swampland cobordism conjecture. Across AdS and Minkowski, Type II, M-theory, and non-supersymmetric strings, the naive singularities are resolved by ends of spacetime that trigger spontaneous compactification, often to lower-dimensional ISD-flux backgrounds stabilized by orientifolds, branes, or their variants. The authors illustrate these ideas through explicit constructions: fluxed conifolds (KS/KT), IIB flux compactifications, magnetized branes, massive IIA and USP(32) theories, and M-theory on K3, highlighting how cobordism defects act as the dynamical endpoints of tadpole backreaction. A highlight is a 6d-to-4d scenario in which MSSM-like physics emerges on cobordism branes, hinting at a concrete route by which realistic low-energy physics can arise from spontaneous compactification guided by swampland principles. Overall, the work strengthens the link between dynamical tadpoles, cobordism, and spontaneous compactification, offering a unifying framework with potential implications for phenomenology and cosmology.

Abstract

We consider string theory vacua with tadpoles for dynamical fields and uncover universal features of the resulting spacetime-dependent solutions. We argue that the solutions can extend only a finite distance $Δ$ away in the spacetime dimensions over which the fields vary, scaling as $Δ^n\sim {\cal T}$ with the strength of the tadpole ${\cal T}$. We show that naive singularities arising at this distance scale are physically replaced by ends of spacetime, related to the cobordism defects of the swampland cobordism conjecture and involving stringy ingredients like orientifold planes and branes, or exotic variants thereof. We illustrate these phenomena in large classes of examples, including AdS$_5\times T^{1,1}$ with 3-form fluxes, 10d massive IIA, M-theory on K3, the 10d non-supersymmetric $USp(32)$ strings, and type IIB compactifications with 3-form fluxes and/or magnetized D-branes. We also describe a 6d string model whose tadpole triggers spontaneous compactification to a semirealistic 3-family MSSM-like particle physics model.