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Harvard spokesman Doug Gavel said the university has “fairly strict conflict of interest rules.” He said school policy dictates that the university does not comment on specific faculty members.

It’s unclear who will replace Mr. Carter as the Pentagon’s top weapons buyer, but one possibility is Frank Kendall III, who has served under Mr. Carter as the deputy undersecretary for acquisition, technology and logistics.

Before joining the Pentagon, Mr. Kendall consulted for defense contractor SAIC Inc. and Centra Technology.

However, Mr. Kendall declined to list the identities of six other private-sector clients, The Washington Times reported in 2009.

Federal ethics rules allow nominees to keep the names of former clients a secret in limited circumstances, such as when there was a confidentiality agreement or in matters involving grand jury testimony.

In 2009, the White House stood by Mr. Kendall’s decision not to disclose his past clients, stating in an email that he was “committed to adhering to the highest standards of ethical conduct.”