Navigating collinear superspace
Abstract We introduce a new set of effective field theory rules for constructing Lagrangians with N$$ \mathcal{N} $$ = 1 supersymmetry in collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates xμθαθ†α⋅$$ \left({x}^{\mu },{\theta}^{\alpha },{\theta...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/131715 |
| _version_ | 1811089700709990400 |
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| author | Cohen, Timothy Elor, Gilly Larkoski, Andrew J Thaler, Jesse |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Cohen, Timothy Elor, Gilly Larkoski, Andrew J Thaler, Jesse |
| author_sort | Cohen, Timothy |
| collection | MIT |
| description | Abstract
We introduce a new set of effective field theory rules for constructing Lagrangians with N$$ \mathcal{N} $$ = 1 supersymmetry in collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates xμθαθ†α⋅$$ \left({x}^{\mu },{\theta}^{\alpha },{\theta}^{\dagger \overset{\cdot }{\alpha }}\right) $$, and supersymmetry preservation is manifest at the Lagrangian level in part due to the inclusion of auxiliary F- and D-term components. By contrast, collinear superspace depends on a smaller set of coordinates (xμ, η, η†), where η is a complex Grassmann number without a spinor index. This provides a formulation of supersymmetric theories that depends exclusively on propagating degrees of freedom, at the expense of obscuring Lorentz invariance and introducing inverse momentum scales. After establishing the general framework, we construct collinear superspace Lagrangians for free chiral matter and non-Abelian gauge fields. For the latter construction, an important ingredient is a superfield representation that is simultaneously chiral, anti-chiral, and real; this novel object encodes residual gauge transformations on the light cone. Additionally, we discuss a fundamental obstruction to constructing inter- acting theories with chiral matter; overcoming these issues is the subject of our companion paper, where we introduce a larger set of superfields to realize the full range of interactions compatible with N$$ \mathcal{N} $$ = 1. Along the way, we provide a novel framing of reparametrization invariance using a spinor decomposition, which provides insight into this important light-cone symmetry. |
| first_indexed | 2024-09-23T14:23:19Z |
| format | Article |
| id | mit-1721.1/131715 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:23:19Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1317152023-10-13T20:15:40Z Navigating collinear superspace Cohen, Timothy Elor, Gilly Larkoski, Andrew J Thaler, Jesse Massachusetts Institute of Technology. Center for Theoretical Physics Abstract We introduce a new set of effective field theory rules for constructing Lagrangians with N$$ \mathcal{N} $$ = 1 supersymmetry in collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates xμθαθ†α⋅$$ \left({x}^{\mu },{\theta}^{\alpha },{\theta}^{\dagger \overset{\cdot }{\alpha }}\right) $$, and supersymmetry preservation is manifest at the Lagrangian level in part due to the inclusion of auxiliary F- and D-term components. By contrast, collinear superspace depends on a smaller set of coordinates (xμ, η, η†), where η is a complex Grassmann number without a spinor index. This provides a formulation of supersymmetric theories that depends exclusively on propagating degrees of freedom, at the expense of obscuring Lorentz invariance and introducing inverse momentum scales. After establishing the general framework, we construct collinear superspace Lagrangians for free chiral matter and non-Abelian gauge fields. For the latter construction, an important ingredient is a superfield representation that is simultaneously chiral, anti-chiral, and real; this novel object encodes residual gauge transformations on the light cone. Additionally, we discuss a fundamental obstruction to constructing inter- acting theories with chiral matter; overcoming these issues is the subject of our companion paper, where we introduce a larger set of superfields to realize the full range of interactions compatible with N$$ \mathcal{N} $$ = 1. Along the way, we provide a novel framing of reparametrization invariance using a spinor decomposition, which provides insight into this important light-cone symmetry. 2021-09-20T17:29:53Z 2021-09-20T17:29:53Z 2020-02-25 2020-06-26T13:14:59Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131715 Journal of High Energy Physics. 2020 Feb 25;2020(2):146 PUBLISHER_CC en https://doi.org/10.1007/JHEP02(2020)146 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Cohen, Timothy Elor, Gilly Larkoski, Andrew J Thaler, Jesse Navigating collinear superspace |
| title | Navigating collinear superspace |
| title_full | Navigating collinear superspace |
| title_fullStr | Navigating collinear superspace |
| title_full_unstemmed | Navigating collinear superspace |
| title_short | Navigating collinear superspace |
| title_sort | navigating collinear superspace |
| url | https://hdl.handle.net/1721.1/131715 |
| work_keys_str_mv | AT cohentimothy navigatingcollinearsuperspace AT elorgilly navigatingcollinearsuperspace AT larkoskiandrewj navigatingcollinearsuperspace AT thalerjesse navigatingcollinearsuperspace |