Uniqueness and Analytic Structures of Bosonic String Effective Amplitudes

Abstract

We revisit the zero-transcendentality sector of bosonic string effective amplitudes with spin-1 external states, conjectured to correspond to a mass-deformed $(DF{)}^2$ theory, known as the $(DF{)}^2+\text{YM}$ theory. Imposing gauge invariance, locality, and cyclicity under minimal assumptions uniquely fixes a set of dimension-raising operators and leads to a recursive construction of amplitudes from Yang-Mills amplitudes in the $\hat{I}{\pm }^{\prime }\to 0$ limit. At finite $\hat{I}{\pm }^{\prime }$, certain derivative operators dressed with gauge invariant and $\hat{I}{\pm }^{\prime }$-dependent factors, what we call $\text{inverse operators}$, reconstruct the full bosonic string effective amplitudes, yielding compact expressions that universally factorize into tachyon-pole coefficients times Yang-Mills-Scalar amplitudes. This structure holds at arbitrary multiplicity and also extends to the amplitudes of the pure $(DF{)}^2$, $(DF{)}^2+\ddot{I}{•}^3$ and $(DF{)}^2+\text{YM}+\ddot{I}{•}^3$ theories.

12 pages, 5 figures and one ancillary file