Adinkra foundation of component decomposition and the scan for superconformal multiplets in 11D, N $$ \ma
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Springer
Received: February 24, Revised: May 13, Accepted: August 1, Published: September 11,
2020 2020 2020 2020
S. James Gates Jr., Yangrui Hu and S.-N. Hazel Mak Brown Theoretical Physics Center, Box S, 340 Brook Street, Barus Hall, Providence, RI 02912, U.S.A. Department of Physics, Brown University, Box 1843, 182 Hope Street, Barus & Holley, Providence, RI 02912, U.S.A.
E-mail: sylvester [email protected], yangrui [email protected], sze ning [email protected] Abstract: For the first time in the physics literature, the Lorentz representations of all 2,147,483,648 bosonic degrees of freedom and 2,147,483,648 fermionic degrees of freedom in an unconstrained eleven dimensional scalar superfield are presented. Comparisons of the conceptual bases for this advance in terms of component field, superfield, and adinkra arguments, respectively, are made. These highlight the computational efficiency of the adinkra-based approach over the others. It is noted at level sixteen in the 11D, N = 1 scalar superfield, the {65} representation of SO(1,10), the conformal graviton, is present. Thus, adinkra-based arguments suggest the surprising possibility that the 11D, N = 1 scalar superfield alone might describe a Poincar´e supergravity prepotential or semi-prepotential in analogy to one of the off-shell versions of 4D, N = 1 superfield supergravity. We find the 11D, N = 1 scalar superfield contains 1,494 bosonic fields, 1,186 fermionic fields, and a maximum number of 29,334 links connecting them via orbits of the supercharges. Keywords: Supergravity Models, Superspaces ArXiv ePrint: 2002.08502
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)089
JHEP09(2020)089
Adinkra foundation of component decomposition and the scan for superconformal multiplets in 11D, N = 1 superspace
Contents 1 Introduction
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2 Primers before 11D 2.1 Component primer before 11D 2.2 Superfield primer before 11D 2.3 Adinkra primer before 11D
6 6 6 7 9 12 12 13 14 15 18 20
4 11D N = 1 scalar superfield decomposition 4.1 Methodology 1: branching rules for su(32) ⊃ so(11) 4.2 Methodology 2: plethysms 4.3 Component decomposition results 4.4 11D, N = 1 theory to 10D, N = 2A theory: so(11) ⊃ so(10) 4.5 11D, N = 1 Breitenlohner approach 4.6 Using the V gateway
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5 11D, N = 1 Adinkra diagram
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6 Conclusion
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A SO(11) irreducible representations
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B 11D gamma matrix multiplication table B.1 Identities with unique expressions B.2 Identities with multiple expressions
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C Additional useful identities for 11D gamma matrices
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D Fierz identities for analytical expressions of cubic monomials D.1 For {32} θ-monomials D.2 For {320} θ-monomials D.3 For {1, 408} θ-monomials D.4 For {3, 520} θ-monomials
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–i–
JHEP09(2020)089
3 Traditional path to superfield component decompositions 3.1 Quadratic level 3.2 Cubic level 3.2.1 {32} cubic monomials 3.2.2 {320} cubic monomials 3.2.3 {1, 408} cubic monomials 3.2.4 {3, 520} cubic monomials 3.3 Quartic level
E Handicraft approach to
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