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A Soft Theorem from vertex-like operators in BFSS Theory

Davide Laurenzano, John F. Wheater

TL;DR

This work establishes a soft graviton theorem within BFSS matrix theory by formulating a one-dimensional worldline EFT for $D_0$-brane bound states and introducing vertex-like operators that encode gravitons in target space. Using a UV-finite formalism with an auxiliary field, the authors compute correlation functions of these operators and extract leading and subleading soft factors in the large-$N$ limit. The leading term $S^{(-1)}$ reproduces the expected graviton coupling, while the subleading term $S^{(0)}$ decomposes into orbital and spin contributions, consistent with the known soft graviton structure in eleven-dimensional supergravity. The results provide a worldline proof of the BFSS soft theorem, reinforcing the connection between BFSS matrix theory, asymptotic symmetries, and 11D Lorentz invariance, with potential extensions to full matrix dynamics and additional massless fields.

Abstract

In this paper, we derive a soft theorem at leading and subleading orders within the context of BFSS matrix theory. Specifically, we consider the effective field theory describing interactions between bound states of D0-branes at leading order, which are dual to supergraviton interactions in the eleven-dimensional target space. This theory is obtained from BFSS theory by integrating out heavy degrees of freedom in the large-distance limit at one loop. As part of our analysis, we demonstrate that when treated as a one-dimensional quantum field theory with a UV cutoff, the theory is super-renormalizable and all Feynman diagrams converge. Our main result shows that the theory admits vertex-like operators with the correct quantum numbers to represent supergravitons in target space and that their correlation functions exhibit soft factorisation at both leading and subleading orders.

A Soft Theorem from vertex-like operators in BFSS Theory

TL;DR

This work establishes a soft graviton theorem within BFSS matrix theory by formulating a one-dimensional worldline EFT for -brane bound states and introducing vertex-like operators that encode gravitons in target space. Using a UV-finite formalism with an auxiliary field, the authors compute correlation functions of these operators and extract leading and subleading soft factors in the large- limit. The leading term reproduces the expected graviton coupling, while the subleading term decomposes into orbital and spin contributions, consistent with the known soft graviton structure in eleven-dimensional supergravity. The results provide a worldline proof of the BFSS soft theorem, reinforcing the connection between BFSS matrix theory, asymptotic symmetries, and 11D Lorentz invariance, with potential extensions to full matrix dynamics and additional massless fields.

Abstract

In this paper, we derive a soft theorem at leading and subleading orders within the context of BFSS matrix theory. Specifically, we consider the effective field theory describing interactions between bound states of D0-branes at leading order, which are dual to supergraviton interactions in the eleven-dimensional target space. This theory is obtained from BFSS theory by integrating out heavy degrees of freedom in the large-distance limit at one loop. As part of our analysis, we demonstrate that when treated as a one-dimensional quantum field theory with a UV cutoff, the theory is super-renormalizable and all Feynman diagrams converge. Our main result shows that the theory admits vertex-like operators with the correct quantum numbers to represent supergravitons in target space and that their correlation functions exhibit soft factorisation at both leading and subleading orders.
Paper Structure (11 sections, 113 equations, 1 figure)

This paper contains 11 sections, 113 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Theorem
  3. The Formalism
  4. Correlation function in the effective theory
  5. Vertex-like operators
  6. The leading soft term
  7. Subleading term
  8. Orbital Angular Momentum
  9. Spin
  10. Conclusion
  11. UV finiteness of the effective theory

Figures (1)

  • Figure 1: Soft absorption. The dashed line represents a soft $D_0$ brane bound state, while the solid lines represent the hard ones. The big blob represents interactions between hard particles, whereas the small one stands for interactions between a soft and a hard particle.