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

TL;DR

This paper explores string theory vacua with dynamical tadpoles, revealing universal spacetime-dependent solutions that are finite in extent and involve stringy defects, with implications for compactification and the swampland conjecture.

Contribution

It uncovers universal features of solutions with tadpoles, linking spacetime extent to tadpole strength and connecting singularities to cobordism defects in string theory.

Findings

Solutions extend only a finite distance related to tadpole strength.

Singularities are replaced by spacetime ends involving stringy defects.

Examples include various flux compactifications and a 6d model leading to MSSM-like physics.

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 $\Delta$ away in the spacetime dimensions over which the fields vary, scaling as $\Delta^n\sim {\cal T}$ 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.