Landau Analysis of One-Cycle Negative Geometries
Shruti Paranjape, Marcos Skowronek, Marcus Spradlin, Anastasia Volovich, He-Chen Weng
TLDR
Landau analysis proves four-point, one-cycle negative geometries in N=4 super-Yang-Mills theory exhibit singularities only at z=-1, 0, and infinity.
Key contributions
- Applies geometric Landau analysis to four-point, one-cycle negative geometries in N=4 super-Yang-Mills theory.
- Determines the complete singularity structure for these specific quantum field theory contributions.
- Recursively proves singularities exist exclusively at z=-1, 0, and infinity across all loop orders.
- Lays groundwork for non-perturbative resummation of these quantities at next-to-leading order.
Why it matters
Understanding the singularity structure of these geometries is crucial for theoretical physics. This work provides a foundational step towards non-perturbative resummation for these quantities, advancing our comprehension of quantum field theories.
Original Abstract
We use geometric Landau analysis to determine the singularity structure of four-point, one-cycle negative geometries in $\mathcal{N}=4$ super-Yang-Mills theory, which represent certain contributions to the logarithm of the four-point amplitude or equivalently the normalized quadrangular Wilson loop with a Lagrangian insertion. By analyzing the relevant Landau diagrams recursively, we prove that this quantity has singularities only at $z=-1,0$ and $\infty$ to all loop orders. This represents a first step towards obtaining a non-perturbative resummation for this quantity at next-to-leading order in the expansion over cycles.
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