Modular Invariance of Conformal Field Theory on S1×S3 and Circle Fibrations
Abstract
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 π1(S3/Zp →∞)=Z =π1(S1×S2) and the Gromov-Hausdorff distance between S3/Zp →∞ and S1/Zp →∞×S2 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.
- Publication:
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Physical Review Letters
- Pub Date:
- September 2017
- DOI:
- 10.1103/PhysRevLett.119.131601
- arXiv:
- arXiv:1612.05257
- Bibcode:
- 2017PhRvL.119m1601S
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 12 pages