On stable higher spin states in Heterotic String Theories

TL;DR

The paper investigates stable and non-stable higher-spin states in heterotic string theories with extended supersymmetry, focusing on 1/2 BPS HS multiplets in ${\cal N}=4$ (and ${\cal N}=2$) compactifications. It constructs explicit BRST-invariant vertex operators for the first two massive levels in both the left-moving (superstring) and right-moving (bosonic) sectors, and analyzes their representation content under the relevant little groups, including detailed decompositions to ${\rm SO}(9)$ and ${\rm SO}(25)$. A key result is that tree-level tri-linear couplings of two 1/2 BPS HS states cannot produce a lower-spin BPS state, signaling perturbative stability against such decays, while non-BPS HS states can couple to BPS states in a way that depends on the spin and level; the authors then study 4-point amplitudes with two gauge bosons and two HS states to extract form factors, polarization effects, and the graviton/dilaton exchange structure through the Shapiro–Virasoro factor ${\cal F}_{SV}$. The analysis reveals intricate stringy corrections to HS couplings, including a Regge-limit behavior and kinematical singularities in certain polarization choices, emphasizing that HS dynamics in string theory do not admit a straightforward semi-classical gravity interpretation, and offering insights relevant to microscopic BH entropy counts and duality relations. Overall, the work deepens understanding of HS sectors in heterotic strings, providing explicit operator data and scattering results that illuminate stability, interactions, and phenomenology of HS states in highly supersymmetric backgrounds.

Abstract

We study properties of 1/2 BPS Higher Spin states in heterotic compactifications with extended supersymmetry. We also analyze non BPS Higher Spin states and give explicit expressions for physical vertex operators of the first two massive levels. We then study on-shell tri-linear couplings of these Higher Spin states and confirm that BPS states with arbitrary spin cannot decay into lower spin states in perturbation theory. Finally, we consider scattering of vector bosons off higher spin BPS states and extract form factors and polarization effects in various limits.