Why is your wife a-sexual? Has she been to the doctor/psychiatrist to find out if its anything physical/mental? She may not want sex with you anymore but surely she wants sex???? If she doesn't then she'd be very selfish to want you to stay together and force you to go without.
You'd do well to research Open Marriage (google it) and visit some of the forums etc.
Have you asked your wife what she would do if you DO decide to have other sexual partners? I'd be interested in hearing her answer to that question.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion