{"title":"Free fermions, neutrality and modular transformations","authors":"Mbavhalelo Mulokwe and Konstantinos Zoubos","doi":"10.1088/1751-8121/ad77fe","DOIUrl":null,"url":null,"abstract":"With a view towards higher-spin applications, we study the partition function of a free complex fermion in 2d conformal field theory, restricted to the neutral (zero fermion number) sector. This restriction leads to a partial theta function with a combinatoric interpretation in terms of Dyson’s crank of a partition. More crucially, this partition function can be expressed in terms of a q-hypergeometric function with quantum modular properties. This allows us to find its high-temperature asymptotics, including subleading terms which agree with, but also go beyond, what one obtains by imposing neutrality thermodynamically through a chemical potential. We evaluate the asymptotic density of states for this neutral partition function, including the first few subleading terms. Our results should be extendable to more fermions, as well as to higher-spin chemical potentials, which would be of relevance to the higher-spin/minimal model correspondence.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"16 1","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics A: Mathematical and Theoretical","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1751-8121/ad77fe","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
With a view towards higher-spin applications, we study the partition function of a free complex fermion in 2d conformal field theory, restricted to the neutral (zero fermion number) sector. This restriction leads to a partial theta function with a combinatoric interpretation in terms of Dyson’s crank of a partition. More crucially, this partition function can be expressed in terms of a q-hypergeometric function with quantum modular properties. This allows us to find its high-temperature asymptotics, including subleading terms which agree with, but also go beyond, what one obtains by imposing neutrality thermodynamically through a chemical potential. We evaluate the asymptotic density of states for this neutral partition function, including the first few subleading terms. Our results should be extendable to more fermions, as well as to higher-spin chemical potentials, which would be of relevance to the higher-spin/minimal model correspondence.
期刊介绍:
Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.