specifying punctures like e^{2 pi i/3} about loom HOT 6 CLOSED

Hi Andy,

to specify the punctures try using instead
[1, E^(2 * 3.14159 * I/3), E^(4 * 3.14159 * I/3)]
because "Pi" is not yet interpreted (a minor fix that can be quickly implemented in the master branch, but won't be available on the web interface for a while).
Also note the use of the multiplication sign " * " which is important for the parser.

One more thing, in phi_3 there should not be dz^3 when entered in the web UI.

Finally, with these specifications the example will correctly interpret the differentials. But then it will complain that there are no branch points for this theory, so no spectral network.
Please let us know if you still have trouble.

from loom.

Hi Andy,

Information regarding punctures is first saved as a string, and then interpreted by SymPy. So any correct SymPy expression will go through loom. For example, we can use
[1,E^(2*pi*I/3), E^(4*pi*I/3)]
for the punctures that you want to specify. Then as Pietro says loom doesn't find any branch point for the data you specified.

P.S. to Pietro: I guess Andy used dz^3 in his text for us and didn't use it when inputting the data into loom. :)

from loom.

Thanks, that clears it up!

The spectral network in this case actually should not be trivial -- a
puncture with zero residue does emit some walls. You can see that by
making a very small mass deformation, which will have the effect of
putting two branch points very close to the puncture. But this is a new
kind of special case which I guess hasn't yet made it into the code; and
in fact I don't think I know what is the correct general rule to put in
(it might be interesting to work it out!)

from loom.

Oh, I see, that's why loom didn't find any ramification point. I think I implemented a routine that deals with a massless regular puncture, which is exactly what we have when branch points collide with a regular puncture as mass parameters become zero, but it's lost in the middle of many revisions.

I think I know what the general rule is as far as massless regular punctures of A-type spectral networks are concerned, which passed a few nontrivial tests when I studied AD theories. Here is an excerpt from my note:
https://github.com/chan-y-park/loom/blob/master/documentation/s_walls_around_a_regular_puncture.pdf

from loom.

Ah, I see, nice. That agrees with what I expected at least for N=2 and N=3. Is it from a paper of yours, or private notes?

from loom.

The pages above are actually from my thesis, but now I remember that it's just a copy from my paper 1309.3050. :) Please see pp. 9 ~ 10 of the paper.

from loom.