Local supersymmetry without SUSY partners

Abstract

A gauge theory for a superalgebra that includes an internal gauge (G) and local Lorentz algebras, and that could describe the low energy particle phenomenology is constructed. These two symmetries are connected by fermionic supercharges. The system includes an internal gauge connection 1-form $A$, a spin-1/2 Dirac spinor $\psi$, the Lorentz connection $\omega$, and the vielbein $e$. The connection one-form is in the adjoint representation of G, while $\psi$ is in the fundamental. In contrast to standard supergravity, the metric is not a fundamental field and is in the center of the superalgebra: it is not only invariant under the internal gauge group and under Lorentz transformations, but is also invariant under supersymmetry. The features of this theory that mark the difference with standard supersymmetry are: A) The number of fermionic and bosonic states is not necessarily the same; B) There are no superpartners with equal mass, "bosoninos", sleptons and squarks are absent; C) Although this supersymmetry originates in a local gauge theory and gravity is included, there is no gravitino; D) Fermions acquire mass from their coupling to the background or from self-couplings, while bosons remain massless. In odd dimensions, the Chern-Simons form provides an action that is quasi-invariant under the entire superalgebra. In even dimensions, the Yang-Mills form $<F\ast F>$ is the only natural option, and the symmetry breaks down to [G x SO(1,D-1)]. In 4D, the construction follows the Townsend - Mac Dowell-Mansouri approach. Due to the absence of osp(4|2)-invariant traces in four dimensions, the resulting Lagrangian is only invariant under [U(1) x SO(3,1)], and includes a Nambu--Jona-Lasinio term. In this case, the Lagrangian depends on a single dimensionful parameter that fixes Newton's constant, the cosmological constant and the NJL coupling.

arXiv comment24 pages, no figures. Title changed in journal version to "Unconventional supersymmetry and its breaking". Few references added and some paragraphs rewritten from v.1. This version includes two appendices that are not found in the journal version

References in corpus (33)

• A Supersymmetry Primer
• Gauge fields in graphene
• Historical roots of gauge invariance
• Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory
• Search for Supersymmetry at the LHC in Events with Jets and Missing Transverse Energy
• Supersymmetry of the 2+1 black holes
• Conserved charges for gravity with locally AdS asymptotics
• Supersymmetry of Anti-de Sitter Black Holes
• Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion
• Topologically Massive AdS Gravity
• Quantum field theory in curved graphene spacetimes, Lobachevsky geometry, Weyl symmetry, Hawking effect, and all that
• MacDowell-Mansouri gravity and Cartan geometry
• Conserved Charges for Even Dimensional Asymptotically AdS Gravity Theories
• Higher dimensional Chern-Simons supergravity
• New Gauge Supergravity in Seven and Eleven Dimensions
• Consequences of Propagating Torsion in Connection-Dynamic Theories of Gravity
• Graphene and the Zermelo Optical Metric of the BTZ Black Hole
• The Constraint Algebra of Topologically Massive AdS Gravity
• Gauge Supergravities for all Odd Dimensions
• Supersymmetry of a different kind
• Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
• Parallel Transport of Electrons in Graphene Parallels Gravity
• Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008)
• Poincare invariant gravity with local supersymmetry as a gauge theory for the M-algebra
• On the negative spectrum of the 2+1 black hole
• Supersymmetric Particle in a Spacetime with Torsion and the Index Theorem
• General Relativity from a gauged WZW term
• Supersymmetry Phenomenology
• Stable p-branes in Chern-Simons AdS supergravities
• The nNJL model with a fractional Lorentzian regulator in the real time formalism
• Gauged WZW models for space-time groups and gravitational actions
• Reflections and Impressionistic Portrait at the Conference "Frontiers Beyond the Standard Model," FTPI, Oct. 2012
• Geometry and stability of spinning branes in AdS gravity

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• Negative-curvature spacetime solutions for graphene
• $\mathcal{N}$-Extended $D=4$ Supergravity, Unconventional SUSY and Graphene
• Hunting Quantum Gravity with Analogs: the case of graphene
• Supersymmetric 3D model for gravity with $SU(2)$ gauge symmetry, mass generation and effective cosmological constant
• Dynamical Contents of Unconventional Supersymmetry
• Unconventional SUSY and Conventional Physics: A Pedagogical Review
• Unconventional Supersymmetry at the Boundary of AdS_4 Supergravity
• Graphene, Dirac equation and analogue gravity
• Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory
• The BTZ black hole as a Lorentz-flat geometry
• Chiral gauge theory and gravity from unconventional supersymmetry
• Graphene and Black Holes: novel materials to reach the unreachable
• $\mathcal{N}=2$ Extended MacDowell-Mansouri Supergravity
• The three "layers" of graphene monolayer and their analog generalized uncertainty principles
• New Torsional Deformations of Locally AdS${}_3$ Space
• Gauging the superconformal group with a graded dual operator
• On a Five-Dimensional Chern-Simons AdS Supergravity without gravitino
• A black hole solution in conformal supergravity
• Reassessing the foundations of Metric-Affine Gravity
• Massless Rarita-Schwinger equations: Half and three halves spin solution
• Relational Supersymmetry via the Dressing Field Method and Matter-Interaction Supergeometric Framework
• Unconventional Supersymmetry via the Dressing Field Method
• Canonical Deformation of $N=2$ $Ad{S}_4$ SUGRA
• Embedding of the Georgi-Glashow $SU(5)$ model in the superconformal algebra
• Self duality in unconventional conformal supersymmetry
• Spinor solutions of a Chern-Simons model for the superconformal algebra
• Fermionic Solutions of a Five-Dimensional Chern-Simons AdS Supergravity without Gravitino
• Boson-fermion algebraic mapping in second quantization