Gravity = Yang–Mills
This essay’s title is justified by discussing a class of Yang–Mills-type theories of which standard Yang–Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of homotopy algebras, where conventional Yang–Mills theory is the tens...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-11-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/11/2062 |
| _version_ | 1797457598992089088 |
|---|---|
| author | Roberto Bonezzi Christoph Chiaffrino Felipe Díaz-Jaramillo Olaf Hohm |
| author_facet | Roberto Bonezzi Christoph Chiaffrino Felipe Díaz-Jaramillo Olaf Hohm |
| author_sort | Roberto Bonezzi |
| collection | DOAJ |
| description | This essay’s title is justified by discussing a class of Yang–Mills-type theories of which standard Yang–Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of homotopy algebras, where conventional Yang–Mills theory is the tensor product <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">K</mi><mo>⊗</mo><mi mathvariant="fraktur">g</mi></mrow></semantics></math></inline-formula> of a ‘kinematic’ algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">K</mi></semantics></math></inline-formula> with a color Lie algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">g</mi></semantics></math></inline-formula>. The larger class of Yang–Mills-type theories are given by the tensor product of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">K</mi></semantics></math></inline-formula> with more general Lie-type algebras, of which <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">K</mi></semantics></math></inline-formula> itself is an example, up to anomalies that can be canceled for the tensor product with a second copy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi mathvariant="script">K</mi><mo stretchy="false">¯</mo></mover></semantics></math></inline-formula>. Gravity is then given by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">K</mi><mo>⊗</mo><mover accent="true"><mi mathvariant="script">K</mi><mo stretchy="false">¯</mo></mover></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-09T16:24:20Z |
| format | Article |
| id | doaj.art-2908b27d84304d9c9d1a42d0285b281b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T16:24:20Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2908b27d84304d9c9d1a42d0285b281b2023-11-24T15:08:57ZengMDPI AGSymmetry2073-89942023-11-011511206210.3390/sym15112062Gravity = Yang–MillsRoberto Bonezzi0Christoph Chiaffrino1Felipe Díaz-Jaramillo2Olaf Hohm3Institute for Physics, Humboldt University Berlin, Zum Großen Windkanal 6, D-12489 Berlin, GermanyInstitute for Physics, Humboldt University Berlin, Zum Großen Windkanal 6, D-12489 Berlin, GermanyInstitute for Physics, Humboldt University Berlin, Zum Großen Windkanal 6, D-12489 Berlin, GermanyInstitute for Physics, Humboldt University Berlin, Zum Großen Windkanal 6, D-12489 Berlin, GermanyThis essay’s title is justified by discussing a class of Yang–Mills-type theories of which standard Yang–Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of homotopy algebras, where conventional Yang–Mills theory is the tensor product <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">K</mi><mo>⊗</mo><mi mathvariant="fraktur">g</mi></mrow></semantics></math></inline-formula> of a ‘kinematic’ algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">K</mi></semantics></math></inline-formula> with a color Lie algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">g</mi></semantics></math></inline-formula>. The larger class of Yang–Mills-type theories are given by the tensor product of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">K</mi></semantics></math></inline-formula> with more general Lie-type algebras, of which <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">K</mi></semantics></math></inline-formula> itself is an example, up to anomalies that can be canceled for the tensor product with a second copy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi mathvariant="script">K</mi><mo stretchy="false">¯</mo></mover></semantics></math></inline-formula>. Gravity is then given by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">K</mi><mo>⊗</mo><mover accent="true"><mi mathvariant="script">K</mi><mo stretchy="false">¯</mo></mover></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2073-8994/15/11/2062double copyhomotopy algebrasdouble field theory |
| spellingShingle | Roberto Bonezzi Christoph Chiaffrino Felipe Díaz-Jaramillo Olaf Hohm Gravity = Yang–Mills Symmetry double copy homotopy algebras double field theory |
| title | Gravity = Yang–Mills |
| title_full | Gravity = Yang–Mills |
| title_fullStr | Gravity = Yang–Mills |
| title_full_unstemmed | Gravity = Yang–Mills |
| title_short | Gravity = Yang–Mills |
| title_sort | gravity yang mills |
| topic | double copy homotopy algebras double field theory |
| url | https://www.mdpi.com/2073-8994/15/11/2062 |
| work_keys_str_mv | AT robertobonezzi gravityyangmills AT christophchiaffrino gravityyangmills AT felipediazjaramillo gravityyangmills AT olafhohm gravityyangmills |