2016/12/31 by Edgar Shaghoulian · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computer science #Conformal map #Cosmology and Gravitation Theories #Geometry #Mathematics #Modular design #Nonlinear Waves and Solitons #Programming language #hep-th
paper · pdf · doi:10.1103/physrevlett.119.131601
published as Phys. Rev. Lett. 119, 131601 (2017) · 12 pages
openalex created_date 2017/02/03 · openalex publication_date 2017/09/29 · arxiv created 2017/12/10 · arxiv updated 2017/12/12 · openalex updated_date 2026/08/06
I conjecture a high-temperature--low-temperature duality for conformal field theories defined on circle fibrations like S3 and its lens space family. The duality is an exchange between the thermal circle and the fiber circle in the limit where both are small. The conjecture is motivated by the fact that \ensuremathπ1(S3/ℤ_p\ensuremath→\ensuremath∞)=ℤ=\ensuremathπ1(S1\ifmmode×\else\texttimes\fiS2) and the Gromov-Hausdorff distance between S3/ℤ_p\ensuremath→\ensuremath∞ and S1/ℤ_p\ensuremath→\ensuremath∞\ifmmode×\else\texttimes\fiS2 vanishes. Several checks of the conjecture are provided: free fields, N=1 theories in four dimensions (which shows that the Di Pietro--Komargodski supersymmetric Cardy formula and its generalizations are given exactly by a supersymmetric Casimir energy), N=4 super Yang-Mills at strong coupling, and the six-dimensional N=(2,0) theory. For all examples considered, the duality is powerful enough to control the high-temperature asymptotics on the unlensed S3, relating it to the Casimir energy on a highly lensed S3. Such large-order quotients are more generally useful for studying quantum field theory on curved spacetimes.