Abstract
We propose a universal IR formula for the protected three-sphere correlation functions of Higgs and Coulomb branch operators of N = 4 supersymmetric quantum field theories with massive, topologically trivial vacua.
Highlights
Supersymmetric partition functions and supersymmetric indices are powerful and welldeveloped tools to study supersymmetric quantum field theories, their local operators and extended defects
We propose a universal IR formula for the protected three-sphere correlation functions of Higgs and Coulomb branch operators of N = 4 supersymmetric quantum field theories with massive, topologically trivial vacua
They are often computable by generalizations of the supersymmetric localization techniques of [1]. These tools are typically available for theories endowed with a certain minimum amount of supersymmetry, depending on the specific setup, with special structures emerging in more supersymmetric situations
Summary
Supersymmetric partition functions and supersymmetric indices are powerful and welldeveloped tools to study supersymmetric quantum field theories, their local operators and extended defects. The special sphere partition function can be enriched by a variety of BPS observables which are only available in theories with N = 4 supersymmetry. One can either decorate the special sphere partition function by a collection of Coulomb branch local operators at any point along a specific great circle S1 in the S3, or by a collection of Higgs branch operators (see figure 1). These correlators will behave as a twisted trace on the quantized Coulomb or Higgs branch algebras of the 3d theory, as defined in [7,8,9,10]. Individual terms on the right hand side have poles as a function of m and ζ which are absent on the left hand side, and must cancel in the sum
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