4.4 Article

't Hooft anomalies and the holomorphy of supersymmetric partition functions

期刊

JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 8, 页码 -

出版社

SPRINGER
DOI: 10.1007/JHEP08(2019)035

关键词

Anomalies in Field and String Theories; Global Symmetries

资金

  1. Perimeter Institute for Theoretical Physics
  2. Government of Canada through Industry Canada
  3. Province of Ontario through the Ministry of Economic Development Innovation
  4. ERC [682608]
  5. European Research Council (ERC) [682608] Funding Source: European Research Council (ERC)

向作者/读者索取更多资源

We study the dependence of supersymmetric partition functions on continuous parameters for the flavor symmetry group, G(F), for 2d N = (0, 2) and 4d N = 1 supersymmetric quantum field theories. In any diffeomorphism-invariant scheme and in the presence of G(F) 't Hooft anomalies, the supersymmetric Ward identities imply that the partition function has a non-holomorphic dependence on the flavor parameters. We show this explicitly for the 2d torus partition function, ZT2, and for a large class of 4d partition functions on half-BPS four-manifolds, ZM4(- in particular, for)M(4) = S-3 x S-1 and M-4 = Sigma(g) x T-2. We propose a new expression for ZMd-1xS1, which differs from earlier holomorphic results by the introduction of a non-holomorphic Casimir pre-factor. The latter is fixed by studying the high temperature limit of the partition function. Our proposal agrees with the supersymmetric Ward identities, and with explicit calculations of the absolute value of the partition function using a gauge-invariant zeta-function regularization.

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