The Art of Branching: Cobordism Junctions of 10d String Theories

TL;DR

This paper constructs explicit 10-dimensional string theory junctions, demonstrating cobordisms between different theories and exploring their worldsheet descriptions, including complex examples involving various string theories and orientifolds.

Contribution

It provides the first explicit constructions of 10d string theory junctions and their worldsheet descriptions, illustrating cobordisms predicted by the Cobordism Conjecture.

Findings

Constructed explicit 10d string junction configurations.

Identified extra degrees of freedom as dimensions in supercritical string theory.

Presented examples of junctions involving heterotic, type 0, type II, and orientifold theories.

Abstract

We describe the explicit construction of configurations of several 10d string theories joining at a 9d junction, providing a dynamical realization of cobordisms between multiple 10d string theories, predicted by the Cobordism Conjecture. We provide the microscopic worldsheet description of the configuration in a generalization of the `going up and down the RG flow' interpolations recently used in the description of IIA/IIB domain wall. The interpolations involve additional degrees of freedom, which are gapped except at the branch point, at which the gap closes and triggers the branching transition. The extra degrees of freedom admit an interpretation in terms of additional dimensions in a supercritical string theory, which reduces to the 10d junction configuration upon closed tachyon condensation. Quantum corrections of the 2d worldsheet theory turn the junction into a strongly coupled lightlike core whose UV resolution lies beyond worldsheet techniques. We construct explicit examples of junctions of 10d heterotic string theories, type 0, and type II theories and orientifolds thereof. Our explicit examples include junctions of 10d chiral theories whose chiral fields flow between different branches. One particularly nice configuration is a 4-branch junction of the IIB theory, with type I, the non-supersymmetric $USp(32)$ theory and the $U(32)$ orientifold of 0B theory, thus assembling the four non-tachyonic descendants of type 0B theory.