Gravitational Background of Alice-Vortices and R7-Branes

TL;DR

The paper constructs explicit codimension-two Alice-vortex solutions in axio-dilaton gravity, realizing R7-brane backgrounds in type IIB with monodromy $\tau \mapsto -\overline{\tau}$ and asymptotically locally flat geometry. By solving the far-field equations, the authors identify a tunable brane tension $\mu$ and a multipole structure (notably a transverse dipole moment $q$) that sources a conical deficit $\delta = 2\pi\mu$, and they develop scalar, pseudoscalar, and axio-dilaton Green's functions via Born approximation to study scattering off the background. The results show monopole and dipole couplings, plus nontrivial mixing among angular modes, including half-integer shifts for antiperiodic sectors, signaling rich multipole physics on the brane. Together with a qualitative analysis of the worldvolume theory, these findings provide evidence that the R7-brane supports an interacting 8D non-supersymmetric QFT and bolster the Swampland Cobordism perspective that such defects populate quantum gravity. The work also hints at holographic generalizations and potential AdS-like limits, pointing to broader implications for non-supersymmetric branes and their dual field theories.

Abstract

Codimension-two vortex solutions are important solitonic objects in both quantum field theory and gravity. In this paper, we construct a class of codimension-two Alice-vortex solutions in axio-dilaton gravity, in which monodromy around the vortex enacts the axion transformation $C_0 \mapsto -C_0$. In IIB supergravity, this furnishes a class of R7-brane backgrounds of the sort predicted by the Swampland Cobordism Conjecture. Such configurations generically carry an intrinsic dipole moment. We extract additional properties of such branes from scattering probes. These results provide further evidence that the worldvolume theory of an R7-brane is an 8D non-supersymmetric interacting quantum field theory.

Figures (3)

• Figure 1: Monodromy around the $F_L$ R7-brane of type IIB string theory. Here, $x \equiv x^8$ and $y \equiv x^9$ are local coordinates transverse to the R7-brane. The action on the RR potentials is $C_p \mapsto -C_p$. The dashed line indicates a branch cut.
• Figure 2: Left: Geometry of the R7--brane, shown as a codimension--2 source with core radius $r_c<r_0$. The transverse plane has a deficit angle $\delta$. Right: Illustrative sample internal structure of the brane stress--energy; varying stress-energy that generates the dipole moments is indicated by the gradient.
• Figure 3: Depiction of an $\mathrm{SO}(8)$ 7-brane viewed as a bound state of an $F_L$ and $\Omega$ R7-brane. These R7-branes each come with a dipole moment (black arrows) which must be anti-aligned since there is no net dipole for the $\mathrm{SO}(8)$ 7-brane.