Corpus ID: 235458400

Truncated cluster algebras and Feynman integrals with algebraic letters

@inproceedings{He2021TruncatedCA,
  title={Truncated cluster algebras and Feynman integrals with algebraic letters},
  author={Song He and Zhenjie Li and Qinglin Yang},
  year={2021}
}
We propose that the symbol alphabet for classes of planar, dual-conformalinvariant Feynman integrals can be obtained as truncated cluster algebras purely from their kinematics, which correspond to boundaries of (compactifications of) G+(4, n)/T for the n-particle massless kinematics. For one-, two-, three-mass-easy hexagon kinematics with n = 7, 8, 9, we find finite cluster algebras D4, D5 and D6 respectively, in accordance with previous result on alphabets of these integrals. As the main… Expand

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References

SHOWING 1-10 OF 75 REFERENCES
Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
We further exploit the relation between tropical Grassmannians and Gr(4, n) cluster algebras in order to make and refine predictions for the singularities of scattering amplitudes in N = 4 planarExpand
Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras
Multi-loop scattering amplitudes/null polygonal Wilson loops in N = 4 super-Yang-Mills are known to simplify significantly in reduced kinematics, where external legs/edges lie in an 1 + 1 dimensionalExpand
Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals
We continue the study of positive geometries underlying the Grassmannian string integrals , which are a class of “stringy canonical forms”, or stringy integrals, over the positive Grassmannian modExpand
The double pentaladder integral to all orders
A bstractWe compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar N$$ \mathcal{N} $$Expand
Cluster algebras IV: Coefficients
We study the dependence of a cluster algebra on the choice of coefficients. We write general formulas expressing the cluster variables in any cluster algebra in terms of the initial data; theseExpand
A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon
A bstractSeven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These areExpand
Local integrals for planar scattering amplitudes
A bstractRecently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in $ \mathcal{N} = {4} $ SYM has been described, generalizing the BCFW formula for treeExpand
Motivic amplitudes and cluster coordinates
A bstractIn this paper we study motivic amplitudes — objects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, freeExpand
The cosmic Galois group and extended Steinmann relations for planar N = 4 SYM amplitudes
We describe the minimal space of polylogarithmic functions that is required to express the six-particle amplitude in planar N = 4 super-Yang-Mills theory through six and seven loops, in the NMHV andExpand
Jumpstarting the all-loop S-matrix of planar N = 4 super
We derive a set of first-order differential equations obeyed by the S-matrix of planar maximally supersymmetric Yang-Mills theory. The equations, based on the Yangian symmetry of the theory, involveExpand
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