Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Flat space Fermionic Wave-function coeffients

Bo-Ting Chen, Wei-Ming Chen, Yu-tin Huang, Zi-Xun Huang, Yohan Liu

TL;DR

The work demonstrates that tree-level flat-space wavefunction coefficients for fermions can be reconstructed uniquely from the flat-space S-matrix by enforcing correct total- and partial-energy poles and fermionic cutting rules. By developing a boundary-action framework with proper Dirac boundary conditions, deriving WT identities and locality constraints, the authors bootstrap 3- and 4-point WFCs with explicit spinor-helicity results. They show that partial-energy pole residues fix the WFCs consistently with amplitude factorization, and the four-point WFCs require only the S-matrix data, implying no extra flat-space consistency conditions beyond unitarity and locality. The results illuminate how boundary and bulk dynamics align in flat space, and set the stage for extending the program to curved backgrounds in a companion paper.

Abstract

In this work we analyze the analytic structure of tree-level flat-space wavefunction coefficients (WFCs), with particular attention to fermionic operators, and derive cutting rules for internal-fermion lines. Building on these results, we set up an iterative procedure that, starting from the flat-space S-matrix, reconstructs the 3- and 4-point WFCs with the correct partial- and total-energy poles and satisfying the requisite cutting rules. Consequently, the "four-particle test" for flat-space WFCs imposes no additional constraints beyond the consistency of the flat-space S-matrix.

Flat space Fermionic Wave-function coeffients

TL;DR

The work demonstrates that tree-level flat-space wavefunction coefficients for fermions can be reconstructed uniquely from the flat-space S-matrix by enforcing correct total- and partial-energy poles and fermionic cutting rules. By developing a boundary-action framework with proper Dirac boundary conditions, deriving WT identities and locality constraints, the authors bootstrap 3- and 4-point WFCs with explicit spinor-helicity results. They show that partial-energy pole residues fix the WFCs consistently with amplitude factorization, and the four-point WFCs require only the S-matrix data, implying no extra flat-space consistency conditions beyond unitarity and locality. The results illuminate how boundary and bulk dynamics align in flat space, and set the stage for extending the program to curved backgrounds in a companion paper.

Abstract

In this work we analyze the analytic structure of tree-level flat-space wavefunction coefficients (WFCs), with particular attention to fermionic operators, and derive cutting rules for internal-fermion lines. Building on these results, we set up an iterative procedure that, starting from the flat-space S-matrix, reconstructs the 3- and 4-point WFCs with the correct partial- and total-energy poles and satisfying the requisite cutting rules. Consequently, the "four-particle test" for flat-space WFCs imposes no additional constraints beyond the consistency of the flat-space S-matrix.
Paper Structure (37 sections, 197 equations, 2 figures)

This paper contains 37 sections, 197 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Review of Wavefunction Coefficients
  3. Fermionic Wave Function Coefficient
  4. Spinning WFC and projectors
  5. Operator Decomposition
  6. Constrained Boundary Profile
  7. Ward-Takahashi Identity
  8. Locality
  9. Analytic properties in energy variables
  10. Total energy pole
  11. Contact Diagrams
  12. Exchange Diagrams
  13. Cutting Rules and Partial Energy Poles
  14. Alternative Derivation of (Massive) Fermionic Cutting Rules
  15. Bootstrapping (Fermionic) WF coefficients
  16. ...and 22 more sections

Figures (2)

  • Figure 1: The cutting rule for the one-loop two-propagator WFC with two external legs. The internal leg is cut into two external legs with energies color-coded to match \ref{['eq: LoopCutting1']}.
  • Figure 2: The cutting rule of the 1-loop 1-propagator WFC with two external legs. The internal leg is cut into two external legs with energies color-coded to match \ref{['eq: LoopCutting1']}.