What do you mean by "sync some tables"? There are fundamental challenges.
MySQL DB has columnar data in relational tables, where rows can be removed/updated/inserted very efficiently, while Elasticsearch has JSON documents, which must be denormalized, and massive updates/deletes do not perform well.
If you just want to copy table rows in a naive way by primary keys to ES JSON doc IDs from time to time, you can use my JDBC importer https://github.com/jprante/elasticsearch-jdbc/ which basically performs SQL selects. But it depends on the application data model if that is feasible or not.