Branes and the Swampland

TL;DR

This work proposes a brane-probe approach to the Swampland by analyzing anomaly inflow on 2d string worldsheet theories coupled to 10d and 6d ${\cal N}=(1,0)$ supergravities. By extracting the 2d central charges $c_L,c_R$ and current-algebra levels $k_i$ from inflow, and enforcing unitarity bounds such as $\sum_i c_G(k_i) \le c_L$, the authors derive new constraints on candidate theories, ruling out certain abelian 10d theories and several infinite 6d families, while identifying models that remain viable within these bounds. The method reproduces known restrictions and yields new ones (e.g., a bound $N\le9$ for the 6d $SU(N)\times SU(N)$ with bifundamentals), illustrating the power of brane-probe consistency in delineating the landscape from the Swampland. Overall, the paper establishes brane anomaly inflow as a systematic, calculations-based criterion to refine which low-energy theories can arise from quantum gravity.

Abstract

Completeness of the spectrum of charged branes in a quantum theory of gravity naturally motivates the question of whether consistency of what lives on the branes can be used to explain some of the Swampland conditions. In this paper we focus on consistency of what lives on string probes, to show some of the theories with ${\cal N}=(1,0)$ supersymmetry in 10d and 6d, which are otherwise consistent looking, belong to the Swampland. Gravitational and gauge group anomaly inflow on these probes can be used to compute the gravitational central charges $(c_L,c_R)$ as well as the level of the group's current algebra $k_L$. The fact that the left-moving central charge on the string probes should be large enough to allow {\it unitary} representations of the current algebra with a given level, can be used to rule out some theories. This in particular explains why it has not been possible to construct the corresponding theories from string theory.