It is the aim of this book to provide a brief introductory description of the new physical and mathematical ideas involved in formulating supersymmetric theories. The book starts with a physical motivation of supersymmetry, a presentation of the mathematics of Lie superalgebras, supergroups and superspace. Techniques for constructing manifestly globally supersymmetric field theories are given, using the superfield formalism. To allow for a clear flow of ideas, the basic ideas and techniques are worked out in low space dimensionalities where the formulae do not obscure the concepts.

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Motivations[ edit ] Direct confirmation would entail production of superpartners in collider experiments, such as the Large Hadron Collider LHC. The first runs of the LHC found no previously-unknown particles other than the Higgs boson which was already suspected to exist as part of the Standard Model , and therefore no evidence for supersymmetry.

Such EDM experiments are also much more scalable than conventional particle accelerators and offer a practical alternative to detecting physics beyond the standard model as accelerator experiments become increasingly costly and complicated to maintain. These findings disappointed many physicists, who believed that supersymmetry and other theories relying upon it were by far the most promising theories for "new" physics, and had hoped for signs of unexpected results from these runs.

Light higgsino pair production in association with hard initial state jet radiation leads to a soft opposite-sign dilepton plus jet plus missing transverse energy signal. The hierarchy problem[ edit ] Supersymmetry close to the electroweak scale ameliorates the hierarchy problem that afflicts the Standard Model.

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[ edit ] The idea that the gauge symmetry groups unify at high-energy is called Grand unification theory.

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[ edit ] TeV-scale supersymmetry augmented with a discrete symmetry typically provides a candidate dark matter particle at a mass scale consistent with thermal relic abundance calculations.

Supersymmetric quantum field theory is often much easier to analyze, as many more problems become mathematically tractable. 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 "loophole" to the Colemanâ€”Mandula theorem , which prohibits spacetime and internal symmetries from being combined in any nontrivial way, for quantum field theories like the Standard Model with very general assumptions.

This supersymmetry did not involve spacetime, that is, it concerned internal symmetry, and was broken badly. Gervais and B. Sakita in , [27] Yu. Golfand and E. Likhtman also in , and D. Volkov and V. Akulov , [28] [ full citation needed ] independently rediscovered supersymmetry in the context of quantum field theory , a radically new type of symmetry of spacetime and fundamental fields, which establishes a relationship between elementary particles of different quantum nature, bosons and fermions, and unifies spacetime and internal symmetries of microscopic phenomena.

Finally, Julius Wess and Bruno Zumino in [30] identified the characteristic renormalization features of four-dimensional supersymmetric field theories, which identified them as remarkable QFTs, and they and Abdus Salam and their fellow researchers introduced early particle physics applications.

The mathematical structure of supersymmetry graded Lie superalgebras has subsequently been applied successfully to other topics of physics, ranging from nuclear physics , [31] [32] critical phenomena , [33] quantum mechanics to statistical physics. It remains a vital part of many proposed theories of physics. It was proposed to solve, amongst other things, the hierarchy problem.

Applications[ edit ] Extension of possible symmetry groups[ edit ] One reason that physicists explored supersymmetry is because it offers an extension to the more familiar symmetries of quantum field theory. Supersymmetries, however, are generated by objects that transform by the spin 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.

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## Supersymmetry

Faekasa Be the first to ask a question about Introduction to Supersymmetry. Yau No preview available â€” Supergravities, locally supersymmetric theories are then considered in 4 and 11 dimensions, in component formalism. Einstein fruend as a gauge theory. Quantum Field Theory Lewis H. The supercurrent and anomaly supermultiplets. Yonatan rated it liked it Feb 11, The book will also be of interest to mathematicians with an interest in theoretical physics.

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## Peter Freund

Motivations[ edit ] Direct confirmation would entail production of superpartners in collider experiments, such as the Large Hadron Collider LHC. The first runs of the LHC found no previously-unknown particles other than the Higgs boson which was already suspected to exist as part of the Standard Model , and therefore no evidence for supersymmetry. Such EDM experiments are also much more scalable than conventional particle accelerators and offer a practical alternative to detecting physics beyond the standard model as accelerator experiments become increasingly costly and complicated to maintain. These findings disappointed many physicists, who believed that supersymmetry and other theories relying upon it were by far the most promising theories for "new" physics, and had hoped for signs of unexpected results from these runs. Light higgsino pair production in association with hard initial state jet radiation leads to a soft opposite-sign dilepton plus jet plus missing transverse energy signal. The hierarchy problem[ edit ] Supersymmetry close to the electroweak scale ameliorates the hierarchy problem that afflicts the Standard Model. The observed hierarchy between the electroweak scale and the Planck scale must be achieved with extraordinary fine tuning.

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## Supersymmetry and Supergravity

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## Introduction to Supersymmetry

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