# Constructing the independent basis of total derivative curvature-dependent terms in $6D$

## TL;DR

This paper develops a basis for total derivative curvature terms in six dimensions, simplifying the understanding of conformal anomalies and surface terms in higher-dimensional spaces.

## Contribution

It constructs a minimal basis of independent total derivative terms in 6D, reducing the set from eight to seven, aiding anomaly integration.

## Key findings

- Reduced the basis of surface terms in 6D from eight to seven.
- Clarified the structure of total derivative terms in 6D.
- Enhanced understanding of conformal anomaly integration in higher dimensions.

## Abstract

Total derivative terms play an important role in the integration of conformal anomaly. In four dimensional space $4D$ there is only one such term, namely $\,{\square}R$. In the case of six dimensions $6D$ the structure of surface terms is more complicated, and it is useful to construct a basis of linear independent total derivative terms. We briefly review the general scheme of integrating anomaly and present the reduction of the minimal set of the surface terms in $6D$ from eight to seven.