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

Figures (3)

• Figure 1: a) Sketch of a 3-branch junction of 10d string theories. b) Depiction of the interplay between multi-branch junctions and ETW boundaries for a single branch.
• Figure 2: a) Structure of the junction of 10d type 0 theories resulting from closed tachyon condensation. Some of the branches may be removed by higher order deformations of the superpotential. b) Structure of the junction of 10d type II and type 0 theories after an orbifold, whose fixed plane is shown in pink. The dashed line correspond to the $Y<0$ image of the $Y>0$ branch under it. The $Y$-branch may be removed by higher order deformations of the superpotential.
• Figure 3: a) The 3-branch junction of three 10d $E_8\times SO(16)$ heterotic theories. The colored planes are fixed under the orbifold actions, and the dashed lines correspond to the images of some of the branches under them. b) The no-trivial flow of chiral fields across the junction, resulting in a bouquet configuration.