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 USp(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.

Dynamical Cobordism and the beginning of time: supercritical strings and tachyon condensation

“…On the other hand, there is substantial progress in understanding the implications of the cobordism conjecture at the dynamical level. The configurations dubbed Dynamical Cobordisms in [16][17][18] (see also [19]) 2 describe spacetime dependent solutions in which the fields run until they hit a real-codimension 1 singularity at finite distance in spacetime, at which certain scalars run off to infinite distance in field space. In several examples of such spatially varying solutions, the timelike singularities had a known string theory UV description, which displayed an end of spacetime.…”

“…In several examples of such spatially varying solutions, the timelike singularities had a known string theory UV description, which displayed an end of spacetime. Remarkably, [18] showed that in the effective theory description these singularities (dubbed end-of-the-world (ETW) branes) follow universal scaling laws, and are characterized by a single critical exponent.…”

“…The paper is organized as follows. In section 2 we recall the Dynamical Cobordisms of [16][17][18], and the structure of the ETW branes in terms of their critical exponent. In section 3 we discuss the timelike linear dilaton background as a time-dependent solution: in section 3.1 we express it as a Dynamical Cobordism with a beginning of time; in section 3.2 we describe the singularity at the beginning of time as an ETW brane; and in section 3.3 we explore its UV description in terms of a timelike tachyon condensate.…”

“…In a series of papers [16][17][18] the analysis of dynamical spacetime-dependent solutions realizing cobordisms to nothing was initiated (see also [19]). Such solutions, from the perspective of the lower-dimensional effective field theory, present universal features that allow them to be described in a general framework as follows.…”

“…One of the highlights of the analysis in [18] is that the solutions near ETW branes behave in a simple way. We quote some of the main expressions encapsulating this…”