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The supersymmetric index in four dimensions

Leonardo Rastelli, Shlomo S. Razamat

Abstract

We review the calculation and properties of the supersymmetric index for four dimensional N=1 theories, illustrating its physical significance in several examples.

The supersymmetric index in four dimensions

Abstract

We review the calculation and properties of the supersymmetric index for four dimensional N=1 theories, illustrating its physical significance in several examples.

Paper Structure

This paper contains 20 sections, 118 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Definition of the index
  3. Index as a trace
  4. Index as a partition function
  5. Computation of the index
  6. Index of sigma models
  7. Index of gauge theories
  8. Index spectroscopy
  9. An example
  10. Dualities and Identities
  11. Symmetries and transformations of the index
  12. ${\cal N}=4$ dualities
  13. Seiberg dualities
  14. Kutasov-Schwimmer dualities
  15. Limits
  16. ...and 5 more sections

Figures (2)

  • Figure 1: Different supersymmetric partition functions in dimensions $4,3,2$ are related by limits of parameters (solid lines) and block decompositions (dashed lines). The $\mathbb{S}^3\times \mathbb{S}^1$ partition function (also known as the four-dimensional index) is one of the simplest and most useful partition functions.
  • Figure 2: An $SU(2)\times SU(2)$ quiver gauge theory.