{"title":"Integrability and BRST invariance from BF topological theory","authors":"A Restuccia, A Sotomayor","doi":"10.1088/1751-8121/acff9b","DOIUrl":null,"url":null,"abstract":"Abstract We consider the Becchi, Rouet, Stora and Tyutin (BRST) invariant effective action of the non-abelian BF topological theory in two dimensions with gauge group <?CDATA $Sl(2,\\mathbb{R})$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>S</mml:mi> <mml:mi>l</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> . By considering different gauge fixing conditions, the zero-curvature field equation gives rise to several well known integrable equations. We prove that each integrable equation together with the associated ghost field evolution equation, obtained from the BF theory, is a BRST invariant system with an infinite sequence of BRST invariant conserved quantities. We construct explicitly the systems and the BRST transformation laws for the Korteweg-de Vries (KdV) sequence (including the KdV, mKdV and CKdV equations) and Harry Dym integrable equation.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"58 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics A","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/1751-8121/acff9b","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Abstract We consider the Becchi, Rouet, Stora and Tyutin (BRST) invariant effective action of the non-abelian BF topological theory in two dimensions with gauge group Sl(2,R) . By considering different gauge fixing conditions, the zero-curvature field equation gives rise to several well known integrable equations. We prove that each integrable equation together with the associated ghost field evolution equation, obtained from the BF theory, is a BRST invariant system with an infinite sequence of BRST invariant conserved quantities. We construct explicitly the systems and the BRST transformation laws for the Korteweg-de Vries (KdV) sequence (including the KdV, mKdV and CKdV equations) and Harry Dym integrable equation.
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