The Operator Spectrum of the Six-dimensional (1,0) Theory

TL;DR

This work uses AdS/CFT to determine the protected operator spectrum of the six-dimensional $(1,0)$ theory with $E_8$ symmetry by mapping to the Kaluza-Klein spectrum on $AdS_7 \times S^4/Z_2$. It develops an oscillator framework for $OSp(6,2|2)$ to classify short multiplets and matches bulk KK modes to boundary operators, including both bulk and $E_8$ twisted-sector states. The analysis reveals how orbifolding introduces new short and long multiplets, clarifies the role of doubletons, and describes how the twisted sector encodes $E_8$ currents and moduli. The results provide a concrete spectral organization for the $(1,0)$ theory, highlighting the interplay between bulk supergravity, boundary operators, and orbifold-induced structure with implications for Coulomb/Higgs branch dynamics.

Abstract

We study the large N operator spectrum of the (1,0) superconformal chiral six-dimensional theory with E_8 global symmetry. This spectrum is dual to the Kaluza-Klein spectrum of supergravity on AdS_7 X S^4/Z_2 with a ten-dimensional E_8 theory at its singular locus. We identify those operators in short multiplets of OSp(6,2|2), whose dimensions are exact for any N. We also discuss more general issues concerning AdS/CFT duality on orbifold supergravity backgrounds.