Wavefunction coefficients from amplitubes
Abstract Given a graph its set of connected subgraphs (tubes) can be defined in two ways: either by considering subsets of edges, or by considering subsets of vertices. We refer to these as binary tubes and unary tubes respectively. Both notions come with a natural compatibility condition between tu...
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2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)064 |
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| author | Ross Glew |
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| description | Abstract Given a graph its set of connected subgraphs (tubes) can be defined in two ways: either by considering subsets of edges, or by considering subsets of vertices. We refer to these as binary tubes and unary tubes respectively. Both notions come with a natural compatibility condition between tubes which differ by a simple adjacency constraint. Compatible sets of tubes are referred to as tubings. By considering the set of binary tubes, and summing over all maximal binary-tubings, one is led to an expression for the flat-space wavefunction coefficients relevant for computing cosmological correlators. On the other hand, considering the set of unary tubes, and summing over all maximal unary-tubings, one is led to expressions recently referred to as amplitubes which resemble the scattering amplitudes of tr(ϕ 3) theory. Due to the similarity between these constructions it is natural to expect a close connection between the wavefunction coefficients and amplitubes. In this paper we study the two definitions of tubing in order to provide a new formula for the flat-space wavefunction coefficient for a single graph as a sum over products of amplitubes. We also show how the expressions for the amplitubes can naturally be understood as a sum over orientations of the underlying graph. Combining these observations we are lead to an expression for the wavefunction coefficient given by a sum over terms we refer to as decorated amplitubes which matches a recently conjectured formula resulting from partial fractions. Motivated by our rewriting of the wavefunction coefficient we introduce a new definition of tubing which makes use of both the binary and unary tubes which we refer to as cut tubings. We explain how each cut tubing induces a decorated orientation of the underlying graph satisfying an acyclic condition and demonstrate how the set of all acyclic decorated orientations for a given graph count the number of basis functions appearing in the kinematic flow. |
| format | Article |
| id | doaj-art-2587e96a6c954341b888badd9826dee3 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-2587e96a6c954341b888badd9826dee32025-08-20T04:01:42ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025711710.1007/JHEP07(2025)064Wavefunction coefficients from amplitubesRoss Glew0Department of Physics, Astronomy and Mathematics, University of HertfordshireAbstract Given a graph its set of connected subgraphs (tubes) can be defined in two ways: either by considering subsets of edges, or by considering subsets of vertices. We refer to these as binary tubes and unary tubes respectively. Both notions come with a natural compatibility condition between tubes which differ by a simple adjacency constraint. Compatible sets of tubes are referred to as tubings. By considering the set of binary tubes, and summing over all maximal binary-tubings, one is led to an expression for the flat-space wavefunction coefficients relevant for computing cosmological correlators. On the other hand, considering the set of unary tubes, and summing over all maximal unary-tubings, one is led to expressions recently referred to as amplitubes which resemble the scattering amplitudes of tr(ϕ 3) theory. Due to the similarity between these constructions it is natural to expect a close connection between the wavefunction coefficients and amplitubes. In this paper we study the two definitions of tubing in order to provide a new formula for the flat-space wavefunction coefficient for a single graph as a sum over products of amplitubes. We also show how the expressions for the amplitubes can naturally be understood as a sum over orientations of the underlying graph. Combining these observations we are lead to an expression for the wavefunction coefficient given by a sum over terms we refer to as decorated amplitubes which matches a recently conjectured formula resulting from partial fractions. Motivated by our rewriting of the wavefunction coefficient we introduce a new definition of tubing which makes use of both the binary and unary tubes which we refer to as cut tubings. We explain how each cut tubing induces a decorated orientation of the underlying graph satisfying an acyclic condition and demonstrate how the set of all acyclic decorated orientations for a given graph count the number of basis functions appearing in the kinematic flow.https://doi.org/10.1007/JHEP07(2025)064Cosmological modelsDifferential and Algebraic GeometryScattering Amplitudes |
| spellingShingle | Ross Glew Wavefunction coefficients from amplitubes Journal of High Energy Physics Cosmological models Differential and Algebraic Geometry Scattering Amplitudes |
| title | Wavefunction coefficients from amplitubes |
| title_full | Wavefunction coefficients from amplitubes |
| title_fullStr | Wavefunction coefficients from amplitubes |
| title_full_unstemmed | Wavefunction coefficients from amplitubes |
| title_short | Wavefunction coefficients from amplitubes |
| title_sort | wavefunction coefficients from amplitubes |
| topic | Cosmological models Differential and Algebraic Geometry Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP07(2025)064 |
| work_keys_str_mv | AT rossglew wavefunctioncoefficientsfromamplitubes |