Unconventional SUSY and Conventional Physics: A Pedagogical Review
Abstract
:1. Introduction
1.1. Local Poincaré Symmetry
1.2. Conventional SUSY
1.3. Gauge SUSY
1.4. Standard and CS Supergravities
2. Unconventional SUSY
2.1. Supersymmetric Connection
2.2. Matter Ansatz
3. u-SUSY in Odd Dimensions
3.1. Three-Dimensional u-SUSYs
3.2. Higher Odd Dimensions
4. u-SUSY in Even Dimensions
- (1)
- The fields in the action cannot be only the connection in , the Lie algebra of G. In addition to the connection, other fields must enter in the Lagrangian. These other fields must combine in a way to make a G-invariant action, or
- (2)
- the Lagrangian is constructed with the -valued connection , but the action is not invariant under the entire group G. The symmetry is broken down to a subgroup because is not an invariant tensor of G but an invariant of . Then, the effective gauge symmetry of the action is and the part of the connection that carries the generators of is the only true gauge connection, while the part corresponding to the broken symmetries are in a vector representation of .
4.1. 4D Gauge Gravities
4.2. Yang–Mills Action and Generalizations
4.3. Four-Dimensional u-SUSY
5. Discussion, Summary, and Outlook
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Alvarez, P.D.; Delage, L.; Valenzuela, M.; Zanelli, J. Unconventional SUSY and Conventional Physics: A Pedagogical Review. Symmetry 2021, 13, 628. https://doi.org/10.3390/sym13040628
Alvarez PD, Delage L, Valenzuela M, Zanelli J. Unconventional SUSY and Conventional Physics: A Pedagogical Review. Symmetry. 2021; 13(4):628. https://doi.org/10.3390/sym13040628
Chicago/Turabian StyleAlvarez, Pedro D., Lucas Delage, Mauricio Valenzuela, and Jorge Zanelli. 2021. "Unconventional SUSY and Conventional Physics: A Pedagogical Review" Symmetry 13, no. 4: 628. https://doi.org/10.3390/sym13040628
APA StyleAlvarez, P. D., Delage, L., Valenzuela, M., & Zanelli, J. (2021). Unconventional SUSY and Conventional Physics: A Pedagogical Review. Symmetry, 13(4), 628. https://doi.org/10.3390/sym13040628