{"title":"An Interacting, Higher Derivative, Boundary Conformal Field Theory","authors":"Christopher P. Herzog, Yanjun Zhou","doi":"arxiv-2409.11072","DOIUrl":null,"url":null,"abstract":"We consider a higher derivative scalar field theory in the presence of a\nboundary and a classically marginal interaction. We first investigate the free\nlimit where the scalar obeys the square of the Klein-Gordon equation. In\nprecisely $d=6$ dimensions, modules generated by $d-2$ and $d-4$ dimensional\nprimaries merge to form a staggered module. We compute the conformal block\nassociated with this module and show that it is a generalized eigenvector of\nthe Casimir operator. Next we include the effect of a classically marginal\ninteraction that involves four scalar fields and two derivatives. The theory\nhas an infrared fixed point in $d=6-{\\epsilon}$ dimensions. We compute boundary\noperator anomalous dimensions and boundary OPE coefficients at leading order in\nthe ${\\epsilon}$ expansion for the allowed conformal boundary conditions.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"187 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - High Energy Physics - Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11072","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a higher derivative scalar field theory in the presence of a
boundary and a classically marginal interaction. We first investigate the free
limit where the scalar obeys the square of the Klein-Gordon equation. In
precisely $d=6$ dimensions, modules generated by $d-2$ and $d-4$ dimensional
primaries merge to form a staggered module. We compute the conformal block
associated with this module and show that it is a generalized eigenvector of
the Casimir operator. Next we include the effect of a classically marginal
interaction that involves four scalar fields and two derivatives. The theory
has an infrared fixed point in $d=6-{\epsilon}$ dimensions. We compute boundary
operator anomalous dimensions and boundary OPE coefficients at leading order in
the ${\epsilon}$ expansion for the allowed conformal boundary conditions.