# Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal N=(0,2)$ Supersymmetric Models

## TL;DR

This paper revisits the NSVZ $eta$ functions in two-dimensional $ ext{(0,2)}$ supersymmetric models, constructing a broad class of anomaly-free models and deriving their exact $eta$ functions by analogy with four-dimensional theories.

## Contribution

It introduces a new class of anomaly-free $ ext{(0,2)}$ supersymmetric models and derives their exact $eta$ functions using gauge formulation and analogy with 4D theories.

## Key findings

- Derived exact $eta$ functions for all models in the class.
- Established the analogy between 2D $ ext{(0,2)}$ models and 4D $ ext{N}=1$ Yang-Mills.
- Compared results with previously studied examples.

## Abstract

The NSVZ $\beta$ functions in two-dimensional $\mathcal N=(0,2)$ supersymmetric models are revisited. We construct and discuss a broad class of such models using the gauge formulation. All of them represent direct analogs of four-dimensional ${\mathcal N} =1$ Yang-Mills theories and are free of anomalies. Following the same line of reasoning as in four dimensions we distinguish between the holomorphic and canonical coupling constants. This allows us to derive the exact two-dimensional $\beta$ functions in all models from the above class. We then compare our results with a few examples which have been studied previously.