Supersymmetry - Wikipedia, the free encyclopedia. In particle physics, supersymmetry (SUSY) is a proposed type of spacetime symmetry that relates two basic classes of elementary particles: bosons, which have an integer- valued spin, and fermions, which have a half- integer spin. In a theory with perfectly . For example, there would be a . Thus, since no superpartners have been observed, if supersymmetry exists it must be a spontaneously broken symmetry so that superpartners may differ in mass. The simplest realization of spontaneously- broken supersymmetry, the so- called Minimal Supersymmetric Standard Model, is one of the best studied candidates for physics beyond the Standard Model. Direct confirmation would entail production of superpartners in collider experiments, such as the Large Hadron Collider (LHC). The first run of the LHC found no evidence for supersymmetry (all results were consistent with the Standard Model), and thus set limits on superpartner masses in supersymmetric theories.
While some remain enthusiastic about supersymmetry. The observed hierarchy between the electroweak scale and the Planck scale must be achieved with extraordinary fine tuning. In a supersymmetric theory, on the other hand, Planck- scale quantum corrections cancel between partners and superpartners (owing to a minus sign associated with fermionic loops). The hierarchy between the electroweak scale and the Planck scale is achieved in a natural manner, without miraculous fine- tuning. Gauge coupling unification. In the Standard Model, however, the weak, strong and electromagnetic couplings fail to unify at high energy. In a supersymmetry theory, the running of the gauge couplings are modified, and precise high- energy unification of the gauge couplings is achieved. The modified running also provides a natural mechanism for radiative electroweak symmetry breaking. Dark matter. Supersymmetric quantum field theory is often much easier to analyze, as many more problems become exactly solvable. When supersymmetry is imposed as a local symmetry, Einstein's theory of general relativity is included automatically, and the result is said to be a theory of supergravity. It is also a necessary feature of the most popular candidate for a theory of everything, superstring theory, and a SUSY theory could explain the issue of cosmological inflation. Another theoretically appealing property of supersymmetry is that it offers the only . The Haag- Lopuszanski- Sohnius theorem demonstrates that supersymmetry is the only way spacetime and internal symmetries can be combined consistently. This supersymmetry did not involve spacetime, that is, it concerned internal symmetry, and was broken badly. Miyazawa's work was largely ignored at the time. Sakita (during 1. Likhtman (also during 1. D. V. Supersymmetry with a consistent Lie- algebraic graded structure on which the Gervais. The mathematical structure of supersymmetry (Graded Lie superalgebras) has subsequently been applied successfully to other topics of physics, ranging from nuclear physics. It remains a vital part of many proposed theories of physics. The first realistic supersymmetric version of the Standard Model was proposed during 1. Pierre Fayet and is known as the Minimal Supersymmetric Standard Model or MSSM for short. Abstract: These are expanded notes of lectures given at the summer school 'Gif 2000' in Paris. They constitute the first part of an 'Introduction to supersymmetry and supergravity' with the second part on. An Introduction to Supersymmetry Ulrich Theis Institute for Theoretical Physics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, D–07743 Jena, Germany [email protected] This is a write-up of a series of 0 R f, L f h 0 h Figure 3: Scalar boson contribution to the Higgs mass term via the trilinear coupling. INTRODUCTION TO SUPERSYMMETRY (PHYS 661) Instructor: Philip Argyres (pronounced “are–JEER–us”) O. Qualitative supersymmetry — 4. It was proposed to solve, amongst other things, the hierarchy problem. Applications. These symmetries are grouped into the Poincar. During 1. 97. 1 Golfand and Likhtman were the first to show that the Poincar. During 1. 97. 5 the Haag- Lopuszanski- Sohnius theorem analyzed all possible superalgebras in the general form, including those with an extended number of the supergenerators and central charges. This extended super- Poincar. Supersymmetries, however, are generated by objects that transform by the spinor representations. According to the spin- statistics theorem, bosonic fields commute while fermionic fields anticommute. Combining the two kinds of fields into a single algebra requires the introduction of a Z2- grading under which the bosons are the even elements and the fermions are the odd elements. Such an algebra is called a Lie superalgebra. The simplest supersymmetric extension of the Poincar. Expressed in terms of two Weyl spinors, has the following anti- commutation relation. In the above expression P. Each Lie algebra has an associated Lie group and a Lie superalgebra can sometimes be extended into representations of a Lie supergroup. The Supersymmetric Standard Model. With the addition of new particles, there are many possible new interactions. The simplest possible supersymmetric model consistent with the Standard Model is the Minimal Supersymmetric Standard Model (MSSM) which can include the necessary additional new particles that are able to be superpartners of those in the Standard Model. One of the main motivations for SUSY comes from the quadratically divergent contributions to the Higgs mass squared. The quantum mechanical interactions of the Higgs boson causes a large renormalization of the Higgs mass and unless there is an accidental cancellation, the natural size of the Higgs mass is the greatest scale possible. This problem is known as the hierarchy problem. Supersymmetry reduces the size of the quantum corrections by having automatic cancellations between fermionic and bosonic Higgs interactions. If supersymmetry is restored at the weak scale, then the Higgs mass is related to supersymmetry breaking which can be induced from small non- perturbative effects explaining the vastly different scales in the weak interactions and gravitational interactions. In many supersymmetric Standard Models there is a heavy stable particle (such as neutralino) which could serve as a weakly interacting massive particle (WIMP) dark matter candidate. The existence of a supersymmetric dark matter candidate is related closely to R- parity. The standard paradigm for incorporating supersymmetry into a realistic theory is to have the underlying dynamics of the theory be supersymmetric, but the ground state of the theory does not respect the symmetry and supersymmetry is broken spontaneously. The supersymmetry break can not be done permanently by the particles of the MSSM as they currently appear. This means that there is a new sector of the theory that is responsible for the breaking. The only constraint on this new sector is that it must break supersymmetry permanently and must give superparticles Te. V scale masses. There are many models that can do this and most of their details do not matter. In order to parameterize the relevant features of supersymmetry breaking, arbitrary soft SUSY breaking terms are added to the theory which temporarily break SUSY explicitly but could never arise from a complete theory of supersymmetry breaking. Gauge- coupling unification. The renormalization group evolution of the three gauge coupling constants of the Standard Model is somewhat sensitive to the present particle content of the theory. These coupling constants do not quite meet together at a common energy scale if we run the renormalization group using the Standard Model. Supersymmetric quantum mechanics often becomes relevant when studying the dynamics of supersymmetric solitons, and due to the simplified nature of having fields which are only functions of time (rather than space- time), a great deal of progress has been made in this subject and it is now studied in its own right. SUSY quantum mechanics involves pairs of Hamiltonians which share a particular mathematical relationship, which are called partner Hamiltonians. This fact can be exploited to deduce many properties of the eigenstate spectrum. It is analogous to the original description of SUSY, which referred to bosons and fermions. The SUSY partner of this Hamiltonian would be . Each boson would have a fermionic partner of equal energy. Supersymmetry: Applications to condensed matter physics. Additionally, SUSY has been applied to disorder averaged systems both quantum and non- quantum (through statistical mechanics), the Fokker- Planck equation being an example of a non- quantum theory. The 'supersymmetry' in all these systems arises from the fact that one is modelling one particle and as such the 'statistics' don't matter. The use of the supersymmetry method provides a mathematical rigorous alternative to the replica trick, but only in non- interacting systems, which attempts to address the so- called 'problem of the denominator' under disorder averaging. For more on the applications of supersymmetry in condensed matter physics see the book. Making use of the analogous mathematical structure of the quantum- mechanical Schr. In this manner, a new class of functional optical structures with possible applications in phase matching, mode conversion. SUSY transformations have been also proposed as a way to address inverse scattering problems in optics and as a one- dimensional transformation optics. This is because it describes complex fields satisfying a property known as holomorphy, which allows holomorphic quantities to be exactly computed. This makes supersymmetric models useful . A prime example of this has been the demonstration of S- duality in four- dimensional gauge theories. It is possible to have multiple supersymmetries and also have supersymmetric extra dimensions. Extended supersymmetry. Theories with more than one supersymmetry transformation are known as extended supersymmetric theories. The more supersymmetry a theory has, the more constrained are the field content and interactions. Typically the number of copies of a supersymmetry is a power of 2, i. In four dimensions, a spinor has four degrees of freedom and thus the minimal number of supersymmetry generators is four in four dimensions and having eight copies of supersymmetry means that there are 3. The maximal number of supersymmetry generators possible is 3. Theories with more than 3. It is not known how to make massless fields with spin greater than two interact, so the maximal number of supersymmetry generators considered is 3.
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