At the End of the World: Local Dynamical Cobordism

Abstract

The Cobordism Conjecture states that any Quantum Gravity configuration admits, at topological level, a boundary ending spacetime. We study the dynamical realization of cobordism, as spacetime dependent solutions of Einstein gravity coupled to scalars containing such end-of-the-world 'branes'. The latter appear in effective theory as a singularity at finite spacetime distance at which scalars go off to infinite field space distance. We provide a local description near the end-of-the-world branes, in which the solutions simplify dramatically and are characterized in terms of a critical exponent, which controls the asymptotic profiles of fields and the universal scaling relations among the spacetime distance to the singularity, the field space distance, and the spacetime curvature. The analysis does not rely on supersymmetry. We study many explicit examples of such Local Dynamical Cobordisms in string theory, including 10d massive IIA, the 10d non-supersymmetric U Sp(32) theory, Bubbles of Nothing, 4d N = 1 cosmic string solutions, the Klebanov-Strassler throat, Dp-brane solutions, brane configurations related to the D1/D5 systems, and small black holes. Our framework encompasses diverse recent setups in which scalars diverge at the core of defects, by regarding them as suitable end-of-the-world branes. We explore the interplay of Local Dynamical Cobordisms with the Distance Conjecture and other swampland constraints.

Supersymmetry breaking, brane dynamics and the swampland

“…1. The existence of the pinchoff singularity appears to be universal [47], and has been recently connected to some swampland conjectures [48][49][50] regarding (the absence of non-trivial) cobordism classes.…”

“…All in all, the results that we have presented in this contribution indicate that brane dynamics can be robust probe for microscopic physics even in the absence of (linear) supersymmetry, at least to some extent. Indeed, deeper connections with holography and swampland conjectures have been explored recently [16,50] from this perspective, complementing the bottom-up considerations of [69,70] (see also [48,49]).…”

Looking for structure in the cobordism conjecture

“…where vol k is the volume of M and g s is the string coupling (see below for a derivation in an example). 11 In a classical regime as considered here, one typically takes g s 1 (see however [5] for less perturbative considerations). If we fix g s to such a value and send vol k → ∞, we deduce from (5.1) that gravity decouples.…”

“…Therefore, the existence of a process connecting any two quantum gravity backgrounds is far from obvious too. Indeed, even if the conjecture is quite recent, already a number of works appeared studying some of its aspects and consequences, including [5][6][7][8][9][10][11]. Bordisms are relevant in several areas in mathematics and physics, a nonexhaustive list of related works is [12][13][14][15][16] for anomalies, [17,18] in relation to bubbles of nothing, [19] for the conjecture in a holographic context.…”

Small Black Hole Explosions

“…The resulting singularities describe physical objects whose properties relate to the infinite distance in interesting ways. In particular, the end of the world branes in dynamical cobordisms [7][8][9][10][11] (see also [12] for the swampland cobordism conjecture, [13][14][15][16] for early work and [17][18][19][20][21][22] for other related recent developments), display interesting scaling relations among the spacetime curvature and the spacetime and field theory distances. Other setups are 4d EFT strings [23][24][25], and small black holes (see e.g.…”