Theory may say that an equity concentration may lead to better board governance as many decisions taken by the board would address the requirement of the major share holder. But we fail to understand that many firms work on market price maximization than the intrinsic value of the share.
There are practical issues that may change the way we look at the relationship. I am attaching the link of a Mc Kinsey insight which may help you in identifying appropriate variables.
Boards whose companies have high debt are likely to scrutinize more financial information of the firms to ensure that they comply with Debt Caveats and avoid negative consequences for any violations.
Governance may have positive or negative relation with Debt-equity (usually a proxy to measure leverage) depending on the overarching institutional set up of the country. On the one hand, lenders would be scrutinising the firm on governance so as to ensure return of their principle (Shleifer and Vishny, 1997) ; whereas, equity enables them to be owners/ or rather partners in the business enabling alignment of interest.
In case of audit committee, the role is to oversee the financial reporting and disclosure process. Further, if the committee is independent, theoretically, their role is further strengthened due to independent or outside view of a third party.As their presence enhances the trust towards the firm; it is expected to have positive relation with governance. However, literature reports mixed results towards having independent directors and performance (economic) of the firm.