All zeros of (super)String Theory

TL;DR

This paper investigates the zeros of string theory amplitudes using a curve-integral representation, revealing connections between bosonic and superstring zeros, supersymmetry, and super-Yang-Mills theory.

Contribution

It introduces a novel curve-integral approach to analyze zeros of string amplitudes, linking bosonic, superstring, and gauge theory results.

Findings

Identifies zeros of bosonic string amplitudes and their relation to kinematic shifts.

Discovers new zeros in super-tachyon amplitudes as supersymmetry avatars.

Recovers super-Yang-Mills theory from fermion amplitude zeros via field theory limit.

Abstract

In this paper, we study the zeros of string theory utilizing its curve-integral representation. Firstly, we note that for bosonic strings the tachyon amplitude in curve-representation is identical to the kinematic shifted Tr$\phi^3$ amplitude. Scaffolding is then equivalent to taking the OPE limit of vertex operators on the string world-sheet, which yields amplitude of higher excitations. Using this picture, we derive that the $n$-point level-$N$ scattering amplitude shares the same set of zeros as the $n$-point tachyon amplitude as well as those inherited from it's prescaffold image, i.e. $(2^N)n$-point. Doing the same for the super-tachyon amplitude, exposes new zeros for the open super-string, which can be viewed as the avatar of supersymmetry. Finally we also consider the gluino amplitude at four and six-points, identifying its zero and recovering super-Yang-Mills via scaffolding. Finally we consider the field theory limit of colored fermion amplitudes from the curve-integral form.