Editing Quantum field theory (section)

====Supersymmetry====
{{Main|Supersymmetry}}

All experimentally known symmetries in nature relate [[boson]]s to bosons and [[fermion]]s to fermions. Theorists have hypothesized the existence of a type of symmetry, called [[supersymmetry]], that relates bosons and fermions.{{r|peskin|zee|page1=795|page2=443}}

The Standard Model obeys [[Poincaré group|Poincaré symmetry]], whose generators are the spacetime [[translation (geometry)|translations]] {{math|''P<sup>μ</sup>''}} and the [[Lorentz transformations]] {{math|''J<sub>μν</sub>''}}.<ref name="WeinbergQFT">{{cite book |last=Weinberg |first=Steven |date=1995 |title=The Quantum Theory of Fields |publisher=Cambridge University Press |isbn=978-0-521-55001-7 |author-link=Steven Weinberg |url-access=registration |url=https://archive.org/details/quantumtheoryoff00stev }}</ref>{{rp|58–60}} In addition to these generators, supersymmetry in (3+1)-dimensions includes additional generators {{math|''Q<sub>α</sub>''}}, called [[supercharge]]s, which themselves transform as [[Weyl fermion]]s.{{r|peskin|zee|page1=795|page2=444}} The symmetry group generated by all these generators is known as the [[super-Poincaré group]]. In general there can be more than one set of supersymmetry generators, {{math|''Q<sub>α</sub><sup>I</sup>'', ''I'' {{=}} 1, ..., ''N''}}, which generate the corresponding {{math|''N'' {{=}} 1}} supersymmetry, {{math|''N'' {{=}} 2}} supersymmetry, and so on.{{r|peskin|zee|page1=795|page2=450}} Supersymmetry can also be constructed in other dimensions,<ref>{{cite arXiv |last1=de Wit |first1=Bernard |last2=Louis |first2=Jan |eprint=hep-th/9801132 |title=Supersymmetry and Dualities in various dimensions |date=1998-02-18 }}</ref> most notably in (1+1) dimensions for its application in [[superstring theory]].<ref>{{cite book |last=Polchinski |first=Joseph |date=2005 |title=String Theory |volume=2 |publisher=Cambridge University Press |isbn=978-0-521-67228-3 |author-link=Joseph Polchinski }}</ref>

The Lagrangian of a supersymmetric theory must be invariant under the action of the super-Poincaré group.{{r|zee|page1=448}} Examples of such theories include: [[Minimal Supersymmetric Standard Model]] (MSSM), [[N {{=}} 4 supersymmetric Yang–Mills theory|{{math|''N'' {{=}} 4}} supersymmetric Yang–Mills theory]],{{r|zee|page1=450}} and superstring theory. In a supersymmetric theory, every fermion has a bosonic [[superpartner]] and vice versa.{{r|zee|page1=444}}

If supersymmetry is promoted to a local symmetry, then the resultant gauge theory is an extension of general relativity called [[supergravity]].<ref name="NathArnowitt">{{cite journal | last1 = Nath | first1 = P. | last2 = Arnowitt | first2 = R. | year = 1975 | title = Generalized Super-Gauge Symmetry as a New Framework for Unified Gauge Theories | journal = Physics Letters B | volume = 56 | issue = 2| page = 177 | doi=10.1016/0370-2693(75)90297-x| bibcode = 1975PhLB...56..177N }}</ref>

Supersymmetry is a potential solution to many current problems in physics. For example, the [[hierarchy problem]] of the Standard Model—why the mass of the Higgs boson is not radiatively corrected (under renormalization) to a very high scale such as the [[Grand Unified Theory|grand unified scale]] or the [[Planck mass|Planck scale]]—can be resolved by relating the [[Higgs field]] and its super-partner, the [[Higgsino]]. Radiative corrections due to Higgs boson loops in Feynman diagrams are cancelled by corresponding Higgsino loops. Supersymmetry also offers answers to the grand unification of all gauge coupling constants in the Standard Model as well as the nature of [[dark matter]].{{r|peskin|page1=796–797}}<ref>{{Cite journal |last=Munoz |first=Carlos |arxiv=1701.05259 |title=Models of Supersymmetry for Dark Matter |journal=EPJ Web of Conferences |volume=136 |pages=01002 |date=2017-01-18 |bibcode=2017EPJWC.13601002M |doi=10.1051/epjconf/201713601002 |s2cid=55199323 }}</ref>

Nevertheless, experiments have yet to provide evidence for the existence of supersymmetric particles. If supersymmetry were a true symmetry of nature, then it must be a broken symmetry, and the energy of symmetry breaking must be higher than those achievable by present-day experiments.{{r|peskin|zee|page1=797|page2=443}}