OpenAI：2026单负螺旋度胶子树图振幅非零研究报告（英文版）（12页）.pdf

1、Single-minus graviton tree amplitudes are nonzeroAlfredo Guevara,1Alexandru Lupsasca,2,3David Skinner,4Andrew Strominger,5and Kevin Weil2on behalf of OpenAI1Institute for Advanced Study2OpenAI3Vanderbilt University4Cambridge University5Harvard UniversitySingle-minus tree-level n-graviton scattering

2、amplitudes are revisited.Often presumed to vanish,they are shown here to be nonvanishing for certain“half-collinear”configurations existing in Kleinspace or for complexified momenta.A BerendsGiele recursion relation for these amplitudes isderived and solved in a form involving a sum over trees.In a

3、restricted kinematic decay region,thissolution simplifies significantly to an(n2)-fold product of soft factors.It is further shown in thisregion that,combined with suitable analyticity assumptions,the n-graviton amplitude is generatedby a recursive Lw1+Ward identity with the three-graviton amplitude

4、 as a seed.Reconciling Einstein gravity with quantum mechanicsis a central challenge in modern physics.Self-dual grav-ity 1,2 provides a much more manageablewhile stillrichtoy model for addressing this challenge.Quantumeffects are finite,computable,and one-loop exact 3,4.Acomplete solution of quantu

5、m self-dual gravity is conceiv-ably within reach 511 and may shed light on quantumEinstein gravity.Penrose famously solved classical self-dual gravity us-ing twistor theory 12,13 a half-century ago.Thehighly non-trivial solutions are generated by an infinite-dimensional symmetry group known as Lw1+1

6、4,which also appears in Einstein gravity 15,16.It is sometimes stated that the tree amplitudes of self-dual gravity are nonzero only for three or fewer gravitons4.Tree amplitudes are purportedly a repackaging of theclassical solutions.This raises a conundrum:how can therichness of the nonlinear Penr