IIB Explored: Reflection 7-Branes

TL;DR

The work addresses how the Cobordism Conjecture constrains IIB / F-theory, predicting a new non-supersymmetric reflection 7-brane (R7-brane) arising from a duality bundle that includes torus reflections. The authors develop a framework combining bordism data, anomaly inflow, and brane probes to characterize the R7-brane, showing it breaks all SUSY and likely lives at strong coupling with a distinct worldvolume structure, including a massless 3-form and a Weyl fermion as a goldstino. They demonstrate how R7-branes can end on other branes and discuss their merger with familiar 7-branes via deficit-angle constraints, and propose a doubled F-theory construction (FF-theory) to geometrize reflections and jointly accommodate R7-branes with standard IIB backgrounds. Altogether, the paper delivers a consistent picture of a new, strongly coupled, non-supersymmetric sector in string theory with potential implications for high-dimensional CFTs and non-supersymmetric vacua, along with a concrete blueprint (FF-theory) for incorporating reflections into F-theory. The results open avenues for exploring metastable non-supersymmetric configurations and possible fixed points beyond conventional SUSY classifications.

Abstract

The Swampland Cobordism Conjecture successfully predicts the supersymmetric spectrum of 7-branes of IIB / F-theory. Including reflections on the F-theory torus, it also predicts the existence of new non-supersymmetric objects, which we dub reflection 7-branes (R7-branes). We present evidence that these R7-branes only exist at strong coupling. R7-branes serve as end of the world branes for 9D theories obtained from type IIB asymmetric orbifold and Dabholkar-Park orientifold backgrounds, and an anomaly inflow analysis suggests the existence of a gapless Weyl fermion, which would have the quantum numbers of a goldstino. Using general arguments, we conclude that different kinds of branes are able to end on the R7, and accounting for their charge requires exotic localized degrees of freedom, for which the simplest possibility is a massless 3-form field on the R7-brane worldvolume. We also show how to generalize the standard F-theory formalism to account for reflections.

Figures (3)

• Figure 1: Depiction of a bordism $\mathcal{C}$ between two manifold $X$ and $Y$ of one dimension less. The physical interpretation of the cobordism is a topology-changing transition described by a smooth spacetime, that can be treated in the low-energy supergravity. If the underlying theory includes additional structures (orientation, spin, a principal bundle…), we demand these can be extended from $X$ and $Y$ to $\mathcal{C}$.
• Figure 2: Depiction of a lasso configuration encircling an R7-brane. There is an excess charge in the configuration which is carried away to infinity. Shrinking the lasso to the core of the R7-brane, we obtain a string which ends on the R7-brane. We find that an even number of F1-strings can end on an $\Omega$-brane and an even number of D1-strings can end on an $\mathsf{F}_{L}$-brane.
• Figure 3: Here we illustrate a lasso configuration of D3-branes (black lines) surrounding an R7-brane (red dot). Two D3-branes extend off to infinity, and by local charge conservation, they can split off to form a junction. Since the R7-brane sends D3's to anti-D3's, the orientation of charge flow in the junction can reverse, allowing us to close off a "lasso" in passing through the branch cut. It is energetically favorable for this lasso to shrink to small size, leading to a pair of D3-branes which can end on the R7-brane. Similar considerations also hold for $[p,q]$ 7-brane configurations.