Branes and the swampland

Hee-Cheol Kim,Cumrun Vafa,Gary Shiu

doi:10.1103/physrevd.100.066006

Hee-Cheol Kim, Cumrun Vafa + Show 1 more

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https://doi.org/10.1103/physrevd.100.066006

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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.

Highlights

Increasing evidence points to the fact that some consistent-looking theories cannot emerge as the IR limit of a quantum gravitational theory and belong to the swampland
We show that all the theories with N > 9 belong to the swampland by showing that the central charge of the SUðNÞ × SUðNÞ current algebra on certain BPS strings, which should exist due to the completeness assumption for the spectrum in a gravitational theory [9,10], are too Published by the American Physical Society
A half-BPS string coupled to the 10D supergravity gives rise to an N 1⁄4 ð0; 8Þ superconformal field theory (SCFT) at low energy

Summary

INTRODUCTION

Increasing evidence points to the fact that some consistent-looking theories cannot emerge as the IR limit of a quantum gravitational theory and belong to the swampland (see Refs. [1,2] for a recent review for some of the swampland criteria). Anomaly cancellations for six-dimensional (1,0) theories were used to show [8] that there are rather restricted sets of choices for the allowed gauge groups and matter representations Many of these were realized through F theory. The anomaly inflow is characterized by the 4-form anomaly polynomial, which in this case is given by

TrF2i i þ

TrF2i : i ð6Þ

G SUðNÞ SOðNÞ SpðNÞ G2 F4 E6 E7 E8 λ

Consistency conditions

Examples

CONCLUSIONS