Kazunari Shima, Motomu Tsuda
The basic idea and some physical implications of nonlinear supersymmetric general relativity (NLSUSY GR) are presented. NLSUSY GR may give new insights into the origin of mass and the mysterious relations between the cosmology and the low energy particle physics, e.g. the spontaneous SUSY breaking scale, the cosmological constant, the (dark) energy density of the universe and the neutrino mass.
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The basic idea and some physical implications of nonlinear supersymmetric general relativity (NLSUSY GR) are discussed, which give new insights into the origin of mass and the mysterious relations between the cosmology and the low energy particle physics, e.g. the spontaneous SUSY breaking scale, the cosmological constant, the (dark) energy density of the universe and the neutrino mass.
We examine the models with gauge group U(1)^{k-1}\times\prod_{i=1}^k SU(n_i), which are obtained from decomposing the supersymmetry breaking model of Affleck, Dine and Seiberg containing an antisymmetric tensor field. We note that all of these models are distinct vacua of a single SU(N) gauge theory with an adjoint superfield. The dynamics of this model may be analyzed using the duality of Kutasov and Schwimmer and the deconfinement trick of Berkooz. This analysis leads to a simple picture for supersymmetry breaking for k=2, complementing that of previous work. We examine the flat directions o…
Nonlinear supersymmetric(NLSUSY) general relativity(GR) is considered and a new fundamental action of the vacuum Einstein-Hilbert(EH)-type is obtained by the Einstein gravity analogue geomtrical arguments on new spacetime inspired by NLSUSY. The new action of NLSUSY GR is unstable and breaks spontaneously to EH action with matter(or New spacetime is unstable and induces spontaneously the phase transition to Riemann spacetime with matter), which may be the real shape of the big bang of the universe and give naturally the unified description of spacetime and matter. Some implications for the low…
The Einstein-Hilbert-type action for nonlinear supersymmetric(NLSUSY) general relativity(GR) proposed as the fundamental action for nature is written down explicitly in terms of the fundamental fields, the graviton and the Nambu-Goldstone(NG) fermion(superons). For comparisons the expansion of the action is carried out by using the affine connection formalism and the spin connection formalism. The linearization of NLSUSY GR is considered and carried out explicitly for the N=2 NLSUSY(Volkov-Akulov) model, which reproduce the equivalent renormalizable theory of the gauge vector multiplet of N=2 …
We show that the nonlinear supersymmetric general relativity gives new insights into the origin of mass and elucidates the mysterious relations between the cosmology and the (low energy) particle physics.
A deformed $q$-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra of a $q$-deformed boson. The limit of this algebra when $q$ is a $n$-th root of unity is also studied in detail. By means of a chain rule expansion, the left and right derivatives are identified with the charge $Q$ and covariant derivative $D$ encountered in ordinary/fractional supersymmetry and this leads to new results for these operators. A generalized Be…
This paper explores the use of a deformation by a root of unity as a tool to build models with a finite number of states for applications to quantum gravity. The initial motivation for this work was cosmological breaking of supersymmetry. We explain why the project was unsuccessful. What is left are some observations on supersymmetry for q-bosons, an analogy between black holes in de Sitter and properties of quantum groups, and an observation on a noncommutative quantum mechanics model with two degrees of freedom, depending on one parameter. When this parameter is positive, the spectrum has a …
We study the equations of the motion for Nambu-Goldstone (NG) fermions in the nonlinear representation of supersymmetry (NLSUSY) and show in N-extended NLSUSY that those equations under massless conditions are satisfied, provided the NG fermions are chiral eigenstates. The physical significance of the result is discussed in the context of NLSUSY general relativity through the relations between nonlinear and linear SUSY theories, which gives a new insight into the chiral symmetry for the low energy particle physics.
The mysterious relation between the large scale structure of the universe and the tiny (Planck) scale structure of the particle physics, e.g. the observed mysterious relation between the (dark) energy density (and the dark matter) of the universe and the origin of the tiny neutrino mass (and the SUSY breaking mass scale) of the particle physics may be explained simply by the nonlinear supersymmmetric general relativity theory (NLSUSY GR).
We examine the AdS/CFT correspondence when the gauge theory is considered on a compactified space with supersymmetry breaking boundary conditions. We find that the corresponding supergravity solution has a negative energy, in agreement with the expected negative Casimir energy in the field theory. Stability of the gauge theory would imply that this supergravity solution has minimum energy among all solutions with the same boundary conditions. Hence we are lead to conjecture a new positive energy theorem for asymptotically locally Anti-de Sitter spacetimes. We show that the candidate minimum en…
The particle recently discovered by the CMS and ATLAS collaborations at CERN is almost certainly a Higgs boson, fulfilling a quest that can be traced back to three seminal high energy papers of 1964, but which is intimately connected to ideas in other areas of physics that go back much further. One might oversimplify the history of the features which (i) give mass to the W and Z particles that mediate the weak nuclear interaction, (ii) effectively break gauge invariance, (iii) eliminate physically unacceptable Nambu-Goldstone bosons, and (iv) give mass to fermions (like the electron) by collec…
In the first part of this lecture, some very basic ideas in supersymmetry and supergravity are presented at a level accessible to readers with modest background in quantum field theory and general relativity. The second part is an outline of a recent paper of the author and his collaborators on the AdS/CFT correspondence applied to the ABJM gauge theory with $\cal{N} =8$ supersymmetry.
We show a low energy physical meaning of nonlinear supersymmetric general relativity (NLSUSY GR) in asymptotic Riemann-flat space-time by studying the vacuum structure of N = 2 linear supersymmetry (LSUSY) invariant QED, which is equivalent to N = 2 NLSUSY model, in two dimensional space-time. Two different vacuum field configurations of SO(3,1) isometry describe the two different physical vacua, i.e. one breaks spontaneously both U(1) and SUSY and the other breaks spontaneously SUSY alone, where the latter elucidates the mysterious relations between the cosmology and the (low energy) particle…
These lectures present an introduction to AdS-CFT, and are intended both for begining and more advanced graduate students, which are familiar with quantum field theory and have a working knowledge of their basic methods. Familiarity with supersymmetry, general relativity and string theory is helpful, but not necessary, as the course intends to be as self-contained as possible. I will introduce the needed elements of field and gauge theory, general relativity, supersymmetry, supergravity, strings and conformal field theory. Then I describe the basic AdS-CFT scenario, of ${\cal N}=4 $ Super Yang…
An $N = 1$ supersymmetric version of two dimensional dilaton gravity coupled to matter is considered. It is shown that the linear dilaton vacuum spontaneously breaks half the supersymmetries, leaving broken a linear combination of left and right supersymmetries which squares to time translations. Supersymmetry suggests a spinorial expression for the ADM energy $M$, as found by Witten in four-dimensional general relativity. Using this expression it is proven that ${M}$ is non-negative for smooth initial data asymptotic (in both directions) to the linear dilaton vacuum, provided that the (not ne…
The 19th century Aether died with Special Relativity but was resurrected by General Relativity in the form of dark energy; a tensile material with tension equal to its energy density. Such a material is provided by the D-branes of string-theory; these can support the fields of supersymmetric particle-physics, although their energy density is cancelled by orientifold singularities upon compactification. Dark energy can still arise from supersymmetry-breaking anti-D-branes but it is probably time-dependent. Recent results on time-dependent compactifications to an FLRW universe with late-time acc…
The geometric argument of the general relativity principle can be carried out on (unstable) Riemann space-time just inspired by nonlinear representation of supersymmetry(NLSUSY), where tangent space is specified by Grassmann degrees of freedom $ψ$ for SL(2,C) besides the ordinary Minkowski one $x^{a}$ for SO(1,3) and gives straightforwardly new Einstein-Hilbert(EH)-type action with global NLSUSY invariance(NLSUSYGR)) equipped with the cosmological term. Due to the NLSUSY nature of space-time NLSUSYGR would collapse(Big Collapse) spontaneously to ordinary E-H action of graviton, NLSUSY action o…
On the occasion of a century from the proposal of General relativity by Einstein, I attempt to tackle some open issues in modern cosmology, via a toy but non-trivial model. Specifically, I would like to link together: (i) the smallness of the cosmological constant today, (ii) the evolution of the universe from an inflationary era after the big-bang till now, and (iii) local supersymmetry in the gravitational sector (supergravity) with a broken spectrum at early eras, by making use of the concept of the "running vacuum" in the context of a simple toy model of four-dimensional N=1 supergravity. …
Supergravity is a remarkable theory combining supersymmetry and general relativity. While the theory has many developers from across the globe, we wish to address the question who were the real originators of this fantastic idea.
We discuss composite representations of new supersymmetry (SUSY) algebra under nonlinear (NL) SUSY transformations in curved space-time from the viewpoint of nonlinear supersymmetric general relativity (NLSUSY GR)/ SGM scenario. We show in the linearization of NLSUSY how various basic fields in linear SUSY theories/supergravity are expressed as functionals in terms of a vierbein and Nambu-Goldstone fermion fundamental fields in NLSUSY GR.
"The important thing is not to stop questioning", including the symmetries on which is based the Standard Model
本文基于弗拉托形变哲学，探讨通过形变和量子化反德西特对称性使强子内部对称性从时空涌现，从而为标准模型提供概念基础或质疑。
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