they have to prove theft for a warran?

my ex accused me of going into her home and stealing while they were gone, which i didn't, police have no proof i stole anything, they say that they have a witness that saw me on their street, but i've never met any of our neighbors and don't know anyone, so i don't know how this witness 'knows' it was me, anyway...is that enough cause to warrant an arrest? they can't prove i stole anything and can't prove it was me, just conjectures on her part