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Title: Navigating collinear superspace

Abstract

We introduce a new set of effective field theory rules for constructing Lagrangians with \( \mathcal{N} \) = 1 supersymmetry in collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates \( \left({x}^{\mu },{\theta}^{\alpha },{\theta}^{\dagger \overset{\cdot }{\alpha }}\right) \), 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 ofmore » interactions compatible with \( \mathcal{N} \) = 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.« less

Authors:
 [1];  [2];  [3];  [4]
  1. Univ. of Oregon, Eugene, OR (United States). Inst. of Theoretical Science
  2. Univ. of Washington, Seattle, WA (United States)
  3. Reed College, Portland, OR (United States)
  4. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Harvard Univ., Cambridge, MA (United States)
Publication Date:
Research Org.:
Univ. of Oregon, Eugene, OR (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Univ. of Washington, Seattle, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
OSTI Identifier:
1603792
Alternate Identifier(s):
OSTI ID: 1774033
Grant/Contract Number:  
SC0011640; SC0018191; SC0011637; SC0012567; PHY-0969510
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 2; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Superspaces; Supersymmetric Effective Theories; Supersymmetric Gauge Theory

Citation Formats

Cohen, Timothy, Elor, Gilly, Larkoski, Andrew J., and Thaler, Jesse. Navigating collinear superspace. United States: N. p., 2020. Web. doi:10.1007/JHEP02(2020)146.
Cohen, Timothy, Elor, Gilly, Larkoski, Andrew J., & Thaler, Jesse. Navigating collinear superspace. United States. doi:https://doi.org/10.1007/JHEP02(2020)146
Cohen, Timothy, Elor, Gilly, Larkoski, Andrew J., and Thaler, Jesse. Tue . "Navigating collinear superspace". United States. doi:https://doi.org/10.1007/JHEP02(2020)146. https://www.osti.gov/servlets/purl/1603792.
@article{osti_1603792,
title = {Navigating collinear superspace},
author = {Cohen, Timothy and Elor, Gilly and Larkoski, Andrew J. and Thaler, Jesse},
abstractNote = {We introduce a new set of effective field theory rules for constructing Lagrangians with \( \mathcal{N} \) = 1 supersymmetry in collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates \( \left({x}^{\mu },{\theta}^{\alpha },{\theta}^{\dagger \overset{\cdot }{\alpha }}\right) \), 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 \( \mathcal{N} \) = 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.},
doi = {10.1007/JHEP02(2020)146},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2020,
place = {United States},
year = {2020},
month = {2}
}

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