TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.4.114
TI  - Superstring amplitudes meet surfaceology
PY  - 2025/10/28
UR  - https://www.scipost.org/SciPostPhys.19.4.114
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 4
SP  - 114
A1  - Cao, Qu
AU  - Dong, Jin
AU  - He, Song
AU  - Zhu, Fan
AB  - We reformulate tree-level amplitudes in open superstring theory (type-I) in terms of stringy Tr$(\phi^3)$ amplitudes with various kinematical shifts in the "curve-integral" formulation: while the bosonic-string amplitude with $n$ pairs of "scaffolding" scalars comes from a particularly simple shift of the Tr$(\phi^3)$ one (corresponding to $n$ length-$2$ cycles), the analogous superstring amplitude requires "correction" terms given by bosonic-string amplitudes with longer, even-length "cycles", which are also Tr$(\phi^3)$ ones at shifted kinematics dictated by the cycles; in total it is expressed as a sum of $(2n-3)!!$ shifted amplitudes originated from the expansion of a reduced Pfaffian. 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, which come from length-$2$ cycles and longer ones respectively (the total sum is associated with the expansion a $n× n$ symmetrical determinant); the corresponding prefactors are nested commutators of $2n$-gon kinematical variables, which nicely become traces of field-strengths for those legs corresponding to scalars in the mixed amplitudes. These interesting linear combinations of bosonic string amplitudes must guarantee the cancellation of tachyon poles and $F^3$ vertices etc., and they give new relations between the superstring amplitude and its bosonic-string building blocks to all orders in the $\alpha'$ expansion (the first order gives a new formula for gluon amplitudes with a single $F^3$ insertion in terms of Yang-Mills-scalar amplitudes). We provide both the worldsheet and "curve-integral" derivations, and discuss applications to heterotic and type II cases.
ER  -

@Article{10.21468/SciPostPhys.19.4.114,
	title={{Superstring amplitudes meet surfaceology}},
	author={Qu Cao and Jin Dong and Song He and Fan Zhu},
	journal={SciPost Phys.},
	volume={19},
	pages={114},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.4.114},
	url={https://scipost.org/10.21468/SciPostPhys.19.4.114},
}