Chiral gauge theory and gravity from unconventional supersymmetry
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Springer
Received: May 14, 2020 Accepted: June 30, 2020 Published: July 28, 2020
Pedro D. Alvarez,a Mauricio Valenzuelab and Jorge Zanellib a
Departamento de F´ısica, Universidad de Antofagasta, Aptdo. 02800, Antofagasta, Chile b Centro de Estudios Cient´ıficos (CECs), Av. Arturo Prat 514, Valdivia, Chile
E-mail: [email protected], [email protected], [email protected] Abstract: From a gauge SU(2, 2|2) model with broken supersymmetry, we construct an action for SU(2)×U(1) Yang-Mills theory coupled to gravity and matter in four dimensions. The connection components for AdS boosts and special conformal translations are auxiliary fields and their fixing reduces the theory to two distinct sectors: a vector-like gauge theory with general relativity and a chiral gauge theory where gravity drops out. We discuss some of the main classical features of the model such as the predicted tree level gauge couplings, cosmological constant value, mass-like terms and the Einstein equations. Keywords: Supergravity Models, Supersymmetry Breaking, Classical Theories of Gravity, Gauge Symmetry ArXiv ePrint: 2005.04178
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)205
JHEP07(2020)205
Chiral gauge theory and gravity from unconventional supersymmetry
Contents 1
2 The 2.1 2.2 2.3 2.4 2.5
model Symmetry algebra Connection and curvature Action principle Effective Lagrangian Dilation symmetry
3 4 5 6 7 9
3 Physical contents 3.1 (A)dS vacuum sector 3.1.1 Gravitional effective action 3.1.2 Matter Lagrangian 3.2 Effective bare coupling constants 3.3 Comments on the field equations
9 10 11 11 14 14
4 Summary and outlook
15
A Representation of the su(2, 2|2) superalgebra
16
B Alternative choices for the dual operator
18
C Field equations
19
1
Introduction
Supersymmetry (SUSY) is the largest symmetry of Quantum Field Theory that unifies spacetime and internal symmetries in a nontrivial manner [1, 2], circumventing the no-go theorems of Coleman and Mandula [3]. SUSY generically predicts the necessary presence of fermions and bosons, improves renormalizability, produce viable dark matter candidate models and, if promoted to a local symmetry, can include gravity. For historical and technical reviews, see for example, [4–6]. Historically, the realization that softly broken SUSY can stabilize the mass of the Higgs boson [7, 8], along with gauge coupling unification [9–11], provided a motivation for SUSY unified extensions of the Standard Model [12–15]. The minimal phenomenologically viable model, the Minimal Supersymmetric Standard Model [13, 14], duplicates the particle content of the Standard Model and predicts the masses of the SUSY partners not far above the weak scale when considered as a solution to the hierarchy problem of the scalar sector of the Standard Model [16]. However, ‘natural’ supersymmetric models that predict
–1–
JHEP07(2020)205
1 Introduction
{Q, Q} ∼ ( JAdS ) + ( TInternal ) .
(1.1)
Supergravity models can be constructed using superalgebra-valued gauge con
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