A Test Of The Chiral E8 Current Algebra On A 6D Non-Critical String

TL;DR

The paper tests the realization of the chiral $E_8$ current algebra on 6D non-critical strings by matching 5D BPS spectra, obtained from M-theory on an elliptically fibered Calabi–Yau near the small $E_8$ instanton point, to $E_8$ multiplets. It counts stringy and particle states via wrapped M-branes on 2- and 4-cycles, employing the cohomology of moduli spaces of curves and including reducible (bound) states to complete the $E_8$ representations. The results show that irreducible and reducible curve states reproduce the full ${f 248}$ of $E_8$, with eight Cartan states arising from bound states, and that the left-moving $E_8$ lattice on the wrapped 5-brane encodes the chiral current algebra. This provides a geometrical verification of the E8 current algebra in the F-theory/M-theory description of 6D non-critical strings and connects the 6D CFT data to the 5D BPS spectrum.

Abstract

Compactifying the $E_8$ non-critical string in 6D down to 5D the 6D strings give rise to particles and strings in 5D. Using the dual M-theory description compactified on an elliptically fibered Calabi-Yau we compare some of the 5D BPS states to what one expects from non-critical strings with an $E_8$ chiral current algebra. The $E_8$ multiplets of particle states comprise of 2-branes wrapping on irreducible curves together with bound states of several 2-branes.