https://scholarlywiki.org/index.php?action=history&feed=atom&title=Physics%3A%282%2B1%29-dimensional_topological_gravityPhysics:(2+1)-dimensional topological gravity - Revision history2026-05-21T05:52:21ZRevision history for this page on the wikiMediaWiki 1.44.5https://scholarlywiki.org/index.php?title=Physics:(2%2B1)-dimensional_topological_gravity&diff=2238&oldid=prevWikiHarold: url2023-03-06T05:03:34Z<p>url</p>
<p><b>New page</b></p><div>{{Short description|General relativity in 2+1 dimensions}}<br />
In two spatial and one time dimensions, [[Physics:General relativity|general relativity]] turns out to have no propagating gravitational degrees of freedom. In fact, it can be shown that in a vacuum, spacetime will always be locally flat (or [[De Sitter space|de Sitter]] or [[Anti-de Sitter space|anti-de Sitter]] depending upon the [[Astronomy:Cosmological constant|cosmological constant]]). This makes '''(2+1)-dimensional topological gravity''' (2+1D topological gravity) a [[Physics:Topological quantum field theory|topological theory]] with no gravitational local degrees of freedom.<br />
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Physicists became interested in the relation between Chern–Simons theory and gravity during the 1980s.<ref>{{cite journal | last1 = Achúcarro | first1 = A. | last2 = Townsend | first2 = P. | year = 1986 | title = A Chern-Simons Action for Three-Dimensional anti-De Sitter Supergravity Theories | journal = Phys. Lett. | volume = B180 | issue = 1–2| page = 89 | doi = 10.1016/0370-2693(86)90140-1 | bibcode = 1986PhLB..180...89A }}</ref> <br />
During this period, [[Biography:Edward Witten|Edward Witten]]<ref>{{cite journal | last = Witten | first = Edward | date = 19 Dec 1988 | title = (2+1)-Dimensional Gravity as an Exactly Soluble System | journal = Nuclear Physics B | volume = 311 | issue = 1 | pages = 46&ndash;78 | doi = 10.1016/0550-3213(88)90143-5|bibcode = 1988NuPhB.311...46W| hdl = 10338.dmlcz/143077 | hdl-access = free }}url=http://srv2.fis.puc.cl/~mbanados/Cursos/TopicosRelatividadAvanzada/Witten2.pdf</ref> argued that 2+1D topological gravity is equivalent to a [[Physics:Chern–Simons theory|Chern–Simons theory]] with the [[Physics:Gauge group|gauge group]] <math>SO(2,2)</math> for a negative cosmological constant, and <math>SO(3,1)</math> for a positive one. This theory can be exactly [[Solvable group|solved]], making it a [[Physics:Toy model|toy model]] for [[Physics:Quantum gravity|quantum gravity]]. The [[Killing form]] involves the Hodge dual.<br />
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Witten later changed his mind,<ref>{{cite arXiv| last = Witten | first = Edward | date = 22 June 2007 | title = Three-Dimensional Gravity Revisited | eprint= 0706.3359 | class = hep-th }}</ref> and argued that nonperturbatively 2+1D topological gravity differs from Chern–Simons because the functional measure is only over nonsingular vielbeins. He suggested the CFT dual is a [[Monster group|monster conformal field theory]], and computed the entropy of [[Physics:BTZ black hole|BTZ black hole]]s.<br />
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== References ==<br />
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