Dynamical Cobordism Conjecture: Solutions for End-of-the-World Branes

Abstract

We analyze finite size solutions for a generalized $D$-dimensional Dudas-Mourad (DM) model featuring dynamical cobordism with neutral and charged end-of-the-world (ETW) defect branes. Confirming a dynamical version of the Cobordism Conjecture, we explicitly construct non-isotropic solutions for the latter codimension one branes and show the appearance of a lower bound $\delta \ge 2\sqrt{(D-1)/(D-2)}$ for the critical exponent in the scaling behavior of the distance and the curvature close to the wall. This allows us to make a connection to the (sharpened) Swampland Distance Conjecture and the (Anti-) de Sitter Distance Conjecture. Moreover, BPS orientifold planes appear as special cases in our analysis and the whole picture is consistent with dimensional reduction from ten to $D$ dimensions. An analogous analysis is performed for a generalized Blumenhagen-Font (BF) model featuring neutral codimension two ETW-branes where the same lower bound for the scaling parameter $\delta$ arises.

41 pages, 2 figures, v2: corrected eqs.(2.18),(2.31), added comment below eq.(3.8)

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• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Morse-Bott inequalities, Topology Change and Cobordisms to Nothing
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