Supersymmetry and Noncommutative Geometry
In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far.The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model.This book is intended for mathematical/theoretical physicists with an interest in the applications of noncommutative geometry to supersymmetric field theories.
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adjoint representation almost-commutative geometry auxiliary fields chiral Ciij Cijj coefficients component conjugate corresponding defined degrees of freedom demand denotes depicted in Fig expression extra contributions fermionic fermionic action fifth type finite algebra finite Dirac operator finite Hilbert space finite spectral triple four-scalar gauge bosons gauge field gauge group gaugino mass grading Higgs Higgs boson higgsinos hypercharge inner fluctuations inner product interactions iſ,j JMel JMer JMWR Jºel kinetic terms KO-dimension Krajewski diagram Lemma Majorana mass mass terms matrix MSSM noncommutative geometry notation parameters particle content path Phys Poincaré algebra pre-factors Proof R-parity scalar fields second term second type Sect self-adjoint ſº spectral action spinor Standard Model superpartners supersymmetric action symmetry third term third type trace unimodularity condition vanish yºr yºu