Supersymmetric localization in two dimensions

Understand

This is an introductory review to localization techniques in supersymmetric two-dimensional gauge theories.

• In particular we describe how to construct Lagrangians of N=(2,2) theories on curved spaces, and how to compute their partition functions and certain correlators on the sphere, the hemisphere and other curved backgrounds.
• We also describe how to evaluate the partition function of N=(0,2) theories on the torus, known as the elliptic genus.
• Finally we summarize some of the applications, in particular to probe mirror symmetry and other non-perturbative dualities.