1. A non-transitory computer-accessible storage medium storing program instructions that when executed on one or more processors: receive, at a log-based transaction manager, a transaction descriptor of a requested transaction from a client, wherein the transaction descriptor comprises at least (a) respective read signatures indicative of one or more objects from which data is read during the requested transaction, including a first object at a first data store and a second object at a second data store, (b) a first committed state identifier (CSI) determined based at least in part on a first logical timestamp corresponding to a first previously-committed transaction at the first data store and a second logical timestamp corresponding to a second previously-committed transaction at the second data store, and (c) respective write signatures indicative of one or more objects to which data is to be written in response to a commit of the requested transaction; identify, by the log-based transaction manager using the first CSI, a subset of transaction records stored in a particular persistent log to be examined for conflicts prior to committing the requested transaction, wherein the particular persistent log comprises transaction records corresponding to previously-committed transactions associated with one or more data stores including the first and second source data stores, in response to a determination, by the log-based transaction manager, that none of the objects indicated by the read signatures of the requested transaction have been modified by a write operation indicated in the subset of transaction records, accept the requested transaction for commit.