On expansions of particle/string amplitudes: one-loop particle amplitudes & surfaceology meets superstring

Novel representation of scattering amplitudes reveals a rich relations in particle/string theories. In this talk, I will first introduce a universal expansion for one-loop gluon amplitudes, which holds for general gauge theories with gluons/fermions/scalars in the loops. These amplitudes are expressed as linear combinations of scalar-loop integrands weighted by gauge-invariant building blocks. Then, I will show how tree-level open superstring amplitudes can be constructed from sum of stringy Tr$({\varphi }^3)$ amplitudes with specific kinematic shifts. Upon taking $n$ scaffolding residues, this leads to a new formula of the $n$-gluon superstring amplitude, which is manifestly symmetric in $n-1$ legs, as a gauge-invariant combination of mixed bosonic string amplitudes with gluons and scalars.