What are some common themes in The Sun Also Rises by Ernest Hemingway and Othello by William Shakespeare? How are these themes present in both of the literature?

One theme common to both works is jealousy. Both Othello and Jake feel inadequate in the eyes of the woman they love. This influences their actions and makes them jealous.
Othello is a middle-aged black man who is not sure he can hold onto the love of the beautiful, young, white Desdemona. Iago plays on Othello's insecurities to make him believe Desdemona is having an affair with Cassio.
Likewise, Jake feels insecure about Brett. She loves him, and he loves her, but they can't consummate their relationship because an injury in World War I has left Jake castrated. Brett therefore has affairs with other men. Jake is angry and jealous when Brett has a fling with Robert Cohn, even though he knows Brett loves him, not Cohn. He resents Cohn, whose body is whole because he never fought in the war.
This leads to a second commonality between Jake and Othello, and a second common theme: the role of an honor code in influencing behavior. Both men have been impacted by their war experiences, and both live by a code. Othello's warrior code causes him to put a premium on honor. When he believes his honor has been undermined by Desdemona's supposed infidelity, he decides he must kill her to restore his honor. Jake lives by an honor code as well, often called the Hemingway code, in which he behaves stoically and courageously. He holds Cohn in contempt for not living by that code, and he admires Romero for living with courage and grace. This code influences him to set Brett up with Romero—both because he is jealous of Cohn and because he feels Romero is worthy of Brett.