# Branes and the Swampland

## TL;DR

This paper investigates how the consistency conditions of brane worldvolume theories, especially anomaly inflow and current algebra unitarity, can identify theories in the Swampland that are otherwise seemingly consistent.

## Contribution

It demonstrates that anomaly inflow and unitarity constraints on string probes can exclude certain 10d and 6d supersymmetric theories from the landscape.

## Key findings

- Certain ${
m extbf{N}=(1,0)}$ theories are in the Swampland due to anomaly constraints.
- Unitarity bounds on current algebra levels rule out some candidate theories.
- The approach explains the absence of these theories in string constructions.

## 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.