On-shell diagrams and the geometry of planar N<4 $$ \mathcal{N}<4 $$ SYM theories
Abstract We continue the discussion of the decorated on-shell diagrammatics for planar N<4 $$ \mathcal{N}<4 $$ Supersymmetric Yang-Mills theories started in [1]. In particular, we focus on its relation with the structure of varieties on the Grassmannian. The decoration of the on-shell diagrams...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2017)192 |
| _version_ | 1818536018798706688 |
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| author | Paolo Benincasa David Gordo |
| author_facet | Paolo Benincasa David Gordo |
| author_sort | Paolo Benincasa |
| collection | DOAJ |
| description | Abstract We continue the discussion of the decorated on-shell diagrammatics for planar N<4 $$ \mathcal{N}<4 $$ Supersymmetric Yang-Mills theories started in [1]. In particular, we focus on its relation with the structure of varieties on the Grassmannian. The decoration of the on-shell diagrams, which physically keeps tracks of the helicity of the coherent states propagating along their edges, defines new on-shell functions on the Grassmannian and can introduce novel higher-order singularities, which graphically are reflected into the presence of helicity loops in the diagrams. These new structures turn out to have similar features as in the non-planar case: the related higher-codimension varieties are identified by either the vanishing of one (or more) Plücker coordinates involving at least two non-adjacent columns, or new relations among Plücker coordinates. A distinctive feature is that the functions living on these higher-codimenson varieties can be thought of distributionally as having support on derivative delta-functions. After a general discussion, we explore in some detail the structures of the on-shell functions on Gr(2, 4) and Gr(3, 6) on which the residue theorem allows to obtain a plethora of identities among them. |
| first_indexed | 2024-12-11T18:32:35Z |
| format | Article |
| id | doaj.art-4736b66b490249f7b24fdaa424cf8673 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T18:32:35Z |
| publishDate | 2017-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4736b66b490249f7b24fdaa424cf86732022-12-22T00:54:52ZengSpringerOpenJournal of High Energy Physics1029-84792017-11-0120171113110.1007/JHEP11(2017)192On-shell diagrams and the geometry of planar N<4 $$ \mathcal{N}<4 $$ SYM theoriesPaolo Benincasa0David Gordo1Instituto de Física Teórica, Universidad Autónoma de Madrid/CSICInstituto de Física Teórica, Universidad Autónoma de Madrid/CSICAbstract We continue the discussion of the decorated on-shell diagrammatics for planar N<4 $$ \mathcal{N}<4 $$ Supersymmetric Yang-Mills theories started in [1]. In particular, we focus on its relation with the structure of varieties on the Grassmannian. The decoration of the on-shell diagrams, which physically keeps tracks of the helicity of the coherent states propagating along their edges, defines new on-shell functions on the Grassmannian and can introduce novel higher-order singularities, which graphically are reflected into the presence of helicity loops in the diagrams. These new structures turn out to have similar features as in the non-planar case: the related higher-codimension varieties are identified by either the vanishing of one (or more) Plücker coordinates involving at least two non-adjacent columns, or new relations among Plücker coordinates. A distinctive feature is that the functions living on these higher-codimenson varieties can be thought of distributionally as having support on derivative delta-functions. After a general discussion, we explore in some detail the structures of the on-shell functions on Gr(2, 4) and Gr(3, 6) on which the residue theorem allows to obtain a plethora of identities among them.http://link.springer.com/article/10.1007/JHEP11(2017)192Gauge SymmetryScattering AmplitudesSupersymmetric Gauge Theory |
| spellingShingle | Paolo Benincasa David Gordo On-shell diagrams and the geometry of planar N<4 $$ \mathcal{N}<4 $$ SYM theories Journal of High Energy Physics Gauge Symmetry Scattering Amplitudes Supersymmetric Gauge Theory |
| title | On-shell diagrams and the geometry of planar N<4 $$ \mathcal{N}<4 $$ SYM theories |
| title_full | On-shell diagrams and the geometry of planar N<4 $$ \mathcal{N}<4 $$ SYM theories |
| title_fullStr | On-shell diagrams and the geometry of planar N<4 $$ \mathcal{N}<4 $$ SYM theories |
| title_full_unstemmed | On-shell diagrams and the geometry of planar N<4 $$ \mathcal{N}<4 $$ SYM theories |
| title_short | On-shell diagrams and the geometry of planar N<4 $$ \mathcal{N}<4 $$ SYM theories |
| title_sort | on shell diagrams and the geometry of planar n 4 mathcal n 4 sym theories |
| topic | Gauge Symmetry Scattering Amplitudes Supersymmetric Gauge Theory |
| url | http://link.springer.com/article/10.1007/JHEP11(2017)192 |
| work_keys_str_mv | AT paolobenincasa onshelldiagramsandthegeometryofplanarn4mathcaln4symtheories AT davidgordo onshelldiagramsandthegeometryofplanarn4mathcaln4symtheories |