# Surveying 4d SCFTs twisted on Riemann surfaces

## TL;DR

This paper classifies two-dimensional theories arising from twisting 4d superconformal theories on Riemann surfaces, providing a method to compute their central charges and R-currents using c-extremization.

## Contribution

It offers a comprehensive classification of 2d theories from twisted 4d SCFTs and develops a general c-extremization procedure for their central charges.

## Key findings

- Classification of 2d theories with various supersymmetries
- Explicit formulas for central charges using c-extremization
- Expression of 2d R-current in terms of 4d data

## Abstract

Within the framework of four dimensional conformal supergravity we consider $\mathcal{N}=1,2,3,4$ supersymmetric theories generally twisted along the abelian subgroups of the R-symmetry and possibly other global symmetry groups. Upon compactification on constant curvature Riemann surfaces with arbitrary genus we provide an extensive classification of the resulting two dimensional theories according to the amount of supersymmetry that is preserved. Exploiting the c-extremization prescription introduced in arXiv:1211.4030 we develop a general procedure to obtain the central charge for 2d $\mathcal{N}=(0,2)$ theories and the expression of the corresponding R-current in terms of the original 4d one and its mixing with the other abelian global currents.