I need a \overbracket to illustrate different permutations (quantum field theory)

I have four fields illustrate by \phi_1,\phi_2,\phi_3 and \phi_4. And I need to illustrate the permutation between them with a \overbracket. For example, the permutation between 1 and 3 would look like this:

But then I have to do 1-2 then 1-4 etc.. I search on the web and I could not find a way to do the overbracket by choosing the two numbers that represent the permutation while always showing the 4 fields.
Any idea?
Thank you in advance for your help.