Universal Properties of Cylinder Partition Functions


Di Pietro, L. (2015). Universal Properties of Cylinder Partition Functions. Perimeter Institute. https://pirsa.org/15110015


Di Pietro, Lorenzo. Universal Properties of Cylinder Partition Functions. Perimeter Institute, Nov. 17, 2015, https://pirsa.org/15110015


          @misc{ pirsa_15110015,
            doi = {},
            url = {https://pirsa.org/15110015},
            author = {Di Pietro, Lorenzo},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Universal Properties of Cylinder Partition Functions},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {nov},
            note = {PIRSA:15110015 see, \url{https://pirsa.org}}


We consider 4d N=1 superconformal theories on a cylinder. The partition function on this geometry computes the superconformal index, and can be obtained via the path integral with time direction compactified on a circle and periodic conditions for fermions. We will describe universal formulas for the asymptotics of such partition functions in the limit of very large circle and of very small circle. These limits are completely fixed in terms of coefficients of the Weyl anomaly (a,c). We will explain why supersymmetry is a necessary condition in 4d to establish these higher dimensional analogues of classic results in 2d CFTs. Finally we will discuss some applications and the extension to 6d.