A four-dimensional conformal construction of Virasoro-Shapiro amplitudes

TL;DR

This paper constructs a four-dimensional conformal amplitude matching string theory's Virasoro-Shapiro form using only conformal field theory principles, offering a new, symmetry-based realization of string-like amplitudes.

Contribution

It introduces a novel four-dimensional conformal amplitude that reproduces string theory amplitudes without relying on worldsheet or string degrees of freedom.

Findings

The amplitude matches the Virasoro-Shapiro form in four dimensions.

The construction is based solely on conformal symmetry, scale invariance, and analyticity.

Provides a new framework for amplitude bootstrap approaches.

Abstract

We construct a four-dimensional conformal amplitude whose four-point structure matches the Virasoro-Shapiro form familiar from string theory. The construction uses only general principles of conformal field theory - radial quantization, scale invariance, and analyticity - and does not rely on worldsheet geometry or string degrees of freedom. The resulting object is a kinematical, first quantized amplitude defined by symmetry and consistency, providing a four-dimensional realization of stringlike analytic structure and a concrete target for amplitude bootstrap approaches.