The bosonic string spectrum and the explicit states up to level $10$ from the lightcone and the chaotic behavior of certain string amplitudes

TL;DR

This paper computes the detailed spectrum and states of the bosonic string up to level 10, analyzes their structure, and links the complexity of string amplitudes to the intricate mixtures of these states, revealing chaotic behavior.

Contribution

It provides explicit state constructions up to level 10, analyzes their tensor structures, and explains the chaotic behavior of string amplitudes through detailed state coefficient analysis.

Findings

Explicit bosonic string spectrum up to level 10

Identification of state tensor structures and multiplicities

Connection between state mixtures and chaotic amplitude behavior

Abstract

We compute the irreps and their multiplicities of bosonic string spectrum up to level 10 and we give explicitly the on shell lightcone states which make the irreps. For scalars and vectors we compute the multiplicity up to level 22 and 19 respectively. The first scalar at odd level appears at level 11. For the bosonic string in non critical dimensions we argue that at level $N$ there are always states transforming as tensors with $ s\ge N/2$ indices. Only in critical dimensions there are states with $s\le N/2$. Looking at the explicit coefficients of the combinations needed to make the irreps from the lightcone states we trace the origin of the chaotic behavior of certain cubic amplitudes considered in literature to the extremely precise and sensitive mixtures of states. For example the vectors at level $N=19$ are a linear combinations of states and when the coefficients are normalized to be integer some of them have more than 1200 figures.