GSO Defects: IIA/IIB Walls and the Surprisingly Stable $\mathrm{R}7$-Brane

TL;DR

This work tests the Swampland Cobordism Conjecture by analyzing GSO defects that separate vacua with different worldsheet GSO projections, focusing on IIA/IIB domain walls and F_L R7 vortices. Using long-string EFT and target-space EFT, it derives a consistent picture in which the IIA/IIB wall relates RR potentials to the other theory’s fluxes via mod 2 reductions, and shows BPS D-branes crossing the wall become non-BPS fluxbranes. A central finding is the stability of the $F_L$ R7-brane, identified with a collapsed cylindrical wall, while Het$_{rak{so}}$ vortices are unstable and tend to dissolve into flux configurations; the D7/D8 system in Type I and the heterotic S-duals provide complementary checks. Collectively, these results bolster the existence and non-supersymmetric stability of GSO defects, with potential implications for non-supersymmetric string vacua and new high-dimensional brane dynamics described by Z$_2$ RR remnants and fluxbranes.

Abstract

The recently proposed Swampland Cobordism Conjecture predicts the existence of new non-supersymmetric objects which supplement the spectrum of low-energy gravitational effective field theories. In this paper, we study a subset of these defects related to the GSO projection on the string worldsheet. These include the predicted domain wall between Type IIA and IIB superstring theories and the newly-discovered $\mathrm{R}7$-brane. We study these defects in two different ways: via long-string probes and target-space effective field theory. We find that the $\mathrm{R}7$-brane can be identified with a collapsed cylindrical configuration of the IIA/IIB wall, and further, that the $\mathrm{R}7$-brane is stable, in contrast to previous expectations. Moreover, we argue that BPS D-branes pulled across the IIA/IIB wall become non-BPS D-branes, which we identify with fluxbrane configurations. We show that the non-BPS D-branes of either Type II theory are charged under a $\mathbb{Z}_2$ remnant of the Ramond-Ramond potentials of the other, which we identify with the mod 2 reduction of the Ramond-Ramond fluxes. Similar considerations provide a complementary perspective on the Heterotic ${\mathfrak{so}(32)}$ S-duals of known non-BPS 7- and 8-branes in Type I string theory.

Figures (15)

• Figure 1: Configuration of a IIA/IIB wall with spatial topology $S^1\times \mathbb{R}^{7}$ and a $(-1)^{F_L}$ monodromy around its 1-cycle, with IIA on the inside and IIB on the outside.
• Figure 2: Target space picture of a long $\mathrm{F}1$-string crossing the IIA/IIB wall.
• Figure 3: Depiction of a GSO interface in type II theory for a long string. In the long string, $g_s \rightarrow 0$ limit we can treat this as a fixed defect in which the choice of GSO projection is different on the two sides of the wall. We have depicted this as a "shaded region" to emphasize that we are remaining agnostic as to the microscopic structure of this interface. That being said, anomaly inflow considerations indicate that anomalies can be cancelled by a 1D Majorana fermion trapped on a thin interface.
• Figure 4: Endability of both of the $(-1)^{F_L}_A$ and $(-1)^{F_L}_B$ topological symmetry operators on the IIA/IIB worldsheet interface.
• Figure 5: Depiction of a long $F1$-string in the vicinity of the IIA/IIB wall. There is a $(-1)^{F_L}$ monodromy cut which emanates out of the wall, leading to a topological operator for $(-1)^{F_L}$ ending on the interface between different GSO projections on the worldvolume of the string.