# Flag manifold sigma-models: the 1/N-expansion and the anomaly two-form

## TL;DR

This paper develops a 1/N-expansion for flag manifold sigma-models, constructs a gauged linear sigma-model representation, and analyzes the quantum anomaly affecting a classically conserved non-local charge.

## Contribution

It introduces a new quantum analysis of flag manifold sigma-models, revealing the anomaly in the non-local charge conservation at the quantum level.

## Key findings

- Explicit calculation of the anomaly in charge conservation
- Development of a gauged linear sigma-model representation
- Establishment of the 1/N-expansion for these models

## Abstract

We construct a gauged linear sigma-model representation and develop a 1/N-expansion for flag manifold sigma-models previously proposed by the author. Classically there exists a zero-curvature representation for the equations of motion of these models, which leads in particular to the existence of a conserved non-local charge. We show that at the quantum level this charge is no longer conserved and calculate explicitly the anomaly in its conservation law.