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 ∆ away in the spacetime dimensions over which the fields vary, scaling as ∆n∼ mathcal{T} with the strength of the tadpole mathcal{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 AdS5×T1,1 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.
Highlights
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
Dynamical tadpoles indicate the fact that equations of motion are not obeyed in the proposed configuration, which should be modified to a spacetime-dependent solution, e.g. rolling down the slope of the potential
These ends of spacetime correspond to cobordism defects of the theory implied by the swampland cobordism conjecture [14, 15]
Summary
We consider the question of dynamical tadpoles and their consequences in a particular setup, based on the gravity dual of the field theory of D3-branes at a coni-. These features (as well as some other upcoming ones) were nicely explained as the gravity dual of a Seiberg duality cascade in [33] This 5d running solution in [32] solves the dynamical tadpole, but is not complete, as it develops a metric singularity at r = r0. This is a physical singularity at finite distance in spacetime, whose parametric dependence on the parameters of the initial model is as follows.
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