Veneziano amplitude in any dimension and a Virasoro-Shapiro partial amplitude

This paper demonstrates how the Veneziano partial amplitude of Bosonic string theory admits a generalization to world-(hyper)surfaces of any dimension <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>d</a:mi></a:math>. In particular, for <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>d</c:mi><c:mo>=</c:mo><c:mn>2</c:mn></c:math>, by carving up the worldsheet integral according to stipulations imposed on conformal cross ratios, the Virasoro-Shapiro full amplitude can be decomposed into a sum of three partial amplitudes. The amplitudes obtained on generalizing the Veneziano amplitude all contain tachyons. To explore candidate tachyon-free and supersymmetric versions of these amplitudes, a new bootstrap principle is introduced and applied, which demands that towers of residues alternate between all-even and all-odd spin partial waves.