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Recently, Mizuno studied generalized Nahm sums associated with symmetrizablematrices. He provided 14 sets of candidates of modular Nahm sums in rank twoand justified four of them. We prove the modularity for eight other sets ofcandidates and present conjectural formulas for the remaining two sets ofcandidates. This is achieved by finding Rogers-Ramanujan type identitiesassociated with these Nahm sums. We also prove Mizuno's conjectural modulartransformation formula for a vector-valued function consists of Nahm sums.Meanwhile, we find some new non-modular identities for some other Nahm sumsassociated with the matrices in Mizuno's candidates.

Proofs of Mizuno's Conjectures on Generalized Rank Two Nahm Sums