Dynamical tadpoles, stringy cobordism, and the SM from spontaneous compactification

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 away in the spacetime dimensions over which the fields vary, scaling as (n)similar to T with the strength of the tadpole 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)xT(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.

Automated summary

This study focuses on string theory vacua with dynamical fields and explores the universal features of the resulting spacetime-dependent solutions. It suggests that these solutions can only extend a finite distance in spacetime dimensions where fields vary, and replaces naive singularities with spacetime ends related to the cobordism defects of the swampland cobordism conjecture involving stringy ingredients.