Sometimes FCLoopFindTopologyMappings cannot find symmetry relations.

[ygtw1]

As follows, "topoA" and "topoB" are identical, and test0, test2, test3, test4 can correctly find the relation but test1 cannot.

<< FeynCalc`

topos = {FCTopology[
"topoA", {SFAD[{{q2, 0}, {0, 1}, 1}],
SFAD[{{q2 + p1, 0}, {1, 1}, 1}], SFAD[{{q1, 0}, {1/16, 1}, 1}],
SFAD[{{q1 + p1/4, 0}, {0, 1}, 1}],
SFAD[{{q2 - p1/4 + p2/2, 0}, {1/16, 1}, 1}],
SFAD[{{q1 + p1/4 - p2/4, 0}, {1/16, 1}, 1}]}, {q1, q2}, {p1,
p2}, {Hold[Pair][Momentum[p1, D], Momentum[p1, D]] -> 1,
Hold[Pair][Momentum[p2, D], Momentum[p1, D]] -> 13/10,
Hold[Pair][Momentum[p2, D], Momentum[p2, D]] -> 1}, {}]};
preferred = {FCTopology[
"topo1", {SFAD[{{q1, 0}, {1, 1}, 1}],
SFAD[{{q1 - p1, 0}, {0, 1}, 1}],
SFAD[{{q2 - p2/4, 0}, {0, 1}, 1}],
SFAD[{{q1 + q2 - p1, 0}, {1/16, 1}, 1}],
SFAD[{{q1 + q2 - p1 + p2/4, 0}, {0, 1}, 1}],
SFAD[{{q1 - (5 p1)/4 + p2/2, 0}, {1/16, 1}, 1}],
SFAD[{{q1 + q2 - (5 p1)/4 + p2/4, 0}, {1/16, 1}, 1}]}, {q1,
q2}, {p1,
p2}, {Hold[Pair][Momentum[p1, D], Momentum[p1, D]] -> 1,
Hold[Pair][Momentum[p2, D], Momentum[p1, D]] -> 13/10,
Hold[Pair][Momentum[p2, D], Momentum[p2, D]] -> 1}, {}],
FCTopology[
"topo2", {SFAD[{{q1, 0}, {1, 1}, 1}],
SFAD[{{q2, 0}, {1/16, 1}, 1}], SFAD[{{q1 - p1, 0}, {0, 1}, 1}],
SFAD[{{q2 - p2/4, 0}, {0, 1}, 1}],
SFAD[{{q1 + q2 - p1, 0}, {1/16, 1}, 1}],
SFAD[{{q1 - (5 p1)/4 + p2/2, 0}, {1/16, 1}, 1}],
SFAD[{{q2 + p1/4 - p2/4, 0}, {1/16, 1}, 1}]}, {q1, q2}, {p1,
p2}, {Hold[Pair][Momentum[p1, D], Momentum[p1, D]] -> 1,
Hold[Pair][Momentum[p2, D], Momentum[p1, D]] -> 13/10,
Hold[Pair][Momentum[p2, D], Momentum[p2, D]] -> 1}, {}],
FCTopology[
"topoB", {SFAD[{{q2, 0}, {0, 1}, 1}],
SFAD[{{q2 + p1, 0}, {1, 1}, 1}], SFAD[{{q1, 0}, {1/16, 1}, 1}],
SFAD[{{q1 + p1/4, 0}, {0, 1}, 1}],
SFAD[{{q2 - p1/4 + p2/2, 0}, {1/16, 1}, 1}],
SFAD[{{q1 + p1/4 - p2/4, 0}, {1/16, 1}, 1}]}, {q1, q2}, {p1,
p2}, {Hold[Pair][Momentum[p1, D], Momentum[p1, D]] -> 1,
Hold[Pair][Momentum[p2, D], Momentum[p1, D]] -> 13/10,
Hold[Pair][Momentum[p2, D], Momentum[p2, D]] -> 1}, {}]};

test0 = FCLoopFindTopologyMappings[topos,
PreferredTopologies ->
preferred[[{1, 2, 3}]], Momentum -> All]
test1 = FCLoopFindTopologyMappings[topos,
PreferredTopologies ->
FCLoopFindSubtopologies@preferred[[{1, 2, 3}]], Momentum -> All]
test2 = FCLoopFindTopologyMappings[topos,
PreferredTopologies ->
FCLoopFindSubtopologies@preferred[[{1,3}]], Momentum -> All]
test3 = FCLoopFindTopologyMappings[topos,
PreferredTopologies ->
FCLoopFindSubtopologies@preferred[[{2, 3}]],
Momentum -> All]
test4 = FCLoopFindTopologyMappings[topos,
PreferredTopologies ->
FCLoopFindSubtopologies@preferred[[{3}]], Momentum -> All]

During evaluation of In[1]:= FeynCalc 10.2.0 (dev version). For help, use the online documentation, visit the forum and have a look at the supplied examples. The PDF-version of the manual can be downloaded here.

During evaluation of In[1]:= If you use FeynCalc in your research, please evaluate FeynCalcHowToCite[] to learn how to cite this software.

During evaluation of In[1]:= Please keep in mind that the proper academic attribution of our work is crucial to ensure the future development of this package!

During evaluation of In[2]:= FCLoopFindTopologyMappings: Found 1 mapping relations

During evaluation of In[2]:= FCLoopFindTopologyMappings: Final number of independent topologies: 1

Out[4]= ({FCTopology(topoA,{1/,1/,1/,1/,1/,1/},{q1,q2},{p1,p2},{Hold[Pair][p1,p1]->1,Hold[Pair][p2,p1]->13/10,Hold[Pair][p2,p2]->1},{}),{q1->q1,q2->q2},G^(topoA)(n1_,n2_,n3_,n4_,n5_,n6_):>G^(topoB)(n1,n2,n3,n4,n5,n6)}
FCTopology(topoB,{1/,1/,1/,1/,1/,1/},{q1,q2},{p1,p2},{Hold[Pair][p1,p1]->1,Hold[Pair][p2,p1]->13/10,Hold[Pair][p2,p2]->1},{})

)

During evaluation of In[2]:= FCLoopFindTopologyMappings: Found 0 mapping relations

During evaluation of In[2]:= FCLoopFindTopologyMappings: Final number of independent topologies: 1

Out[5]= {{},{FCTopology(topoA,{1/,1/,1/,1/,1/,1/},{q1,q2},{p1,p2},{Hold[Pair][p1,p1]->1,Hold[Pair][p2,p1]->13/10,Hold[Pair][p2,p2]->1},{})}}

During evaluation of In[2]:= FCLoopFindTopologyMappings: Found 1 mapping relations

During evaluation of In[2]:= FCLoopFindTopologyMappings: Final number of independent topologies: 1

Out[6]= ({FCTopology(topoA,{1/,1/,1/,1/,1/,1/},{q1,q2},{p1,p2},{Hold[Pair][p1,p1]->1,Hold[Pair][p2,p1]->13/10,Hold[Pair][p2,p2]->1},{}),{q1->q1,q2->q2},G^(topoA)(n1_,n2_,n3_,n4_,n5_,n6_):>G^(topoB)(n1,n2,n3,n4,n5,n6)}
FCTopology(topoB,{1/,1/,1/,1/,1/,1/},{q1,q2},{p1,p2},{Hold[Pair][p1,p1]->1,Hold[Pair][p2,p1]->13/10,Hold[Pair][p2,p2]->1},{})

)

During evaluation of In[2]:= FCLoopFindTopologyMappings: Found 1 mapping relations

During evaluation of In[2]:= FCLoopFindTopologyMappings: Final number of independent topologies: 1

Out[7]= ({FCTopology(topoA,{1/,1/,1/,1/,1/,1/},{q1,q2},{p1,p2},{Hold[Pair][p1,p1]->1,Hold[Pair][p2,p1]->13/10,Hold[Pair][p2,p2]->1},{}),{q1->q1,q2->q2},G^(topoA)(n1_,n2_,n3_,n4_,n5_,n6_):>G^(topoB)(n1,n2,n3,n4,n5,n6)}
FCTopology(topoB,{1/,1/,1/,1/,1/,1/},{q1,q2},{p1,p2},{Hold[Pair][p1,p1]->1,Hold[Pair][p2,p1]->13/10,Hold[Pair][p2,p2]->1},{})

)

During evaluation of In[2]:= FCLoopFindTopologyMappings: Found 1 mapping relations

During evaluation of In[2]:= FCLoopFindTopologyMappings: Final number of independent topologies: 1

Out[8]= ({FCTopology(topoA,{1/,1/,1/,1/,1/,1/},{q1,q2},{p1,p2},{Hold[Pair][p1,p1]->1,Hold[Pair][p2,p1]->13/10,Hold[Pair][p2,p2]->1},{}),{q1->q1,q2->q2},G^(topoA)(n1_,n2_,n3_,n4_,n5_,n6_):>G^(topoB)(n1,n2,n3,n4,n5,n6)}
FCTopology(topoB,{1/,1/,1/,1/,1/,1/},{q1,q2},{p1,p2},{Hold[Pair][p1,p1]->1,Hold[Pair][p2,p1]->13/10,Hold[Pair][p2,p2]->1},{})

)

[vsht]

This one should be also fixed now.

The underlying issue is that not every topology mapping according to the Pak algorithm can be realized via loop momentum shifts. The algorithm treats topologies as if they were loop integrals, so a 1-to-1 relation does not automatically mean that
it will also hold for topologies.

[ygtw1]

Using the updated FeynCalc, the output of

test1 = FCLoopFindTopologyMappings[topos,
PreferredTopologies ->
FCLoopFindSubtopologies@preferred[[{1, 2, 3}]], Momentum -> All]

remains unchanged, and the mapping between topoA and topoB still cannot be established.

I would expect the output to look like the following:
{{{FCTopology[
"topoA", {SFAD[{{q2, 0}, {0, 1}, 1}],
SFAD[{{p1 + q2, 0}, {1, 1}, 1}], SFAD[{{q1, 0}, {1/16, 1}, 1}],
SFAD[{{p1/4 + q1, 0}, {0, 1}, 1}],
SFAD[{{-(p1/4) + p2/2 + q2, 0}, {1/16, 1}, 1}],
SFAD[{{p1/4 - p2/4 + q1, 0}, {1/16, 1}, 1}]}, {q1, q2}, {p1,
p2}, {Hold[Pair][Momentum[p1, D], Momentum[p1, D]] -> 1,
Hold[Pair][Momentum[p2, D], Momentum[p1, D]] -> 13/10,
Hold[Pair][Momentum[p2, D], Momentum[p2, D]] -> 1}, {}], {q1 ->
q1, q2 -> q2},
GLI["topoA", {n1_, n2_, n3_, n4_, n5_, n6_}] :>
GLI["topoB", {n1, n2, n3, n4, n5, n6}]}}, {FCTopology[
"topoB", {SFAD[{{q2, 0}, {0, 1}, 1}],
SFAD[{{p1 + q2, 0}, {1, 1}, 1}], SFAD[{{q1, 0}, {1/16, 1}, 1}],
SFAD[{{p1/4 + q1, 0}, {0, 1}, 1}],
SFAD[{{-(p1/4) + p2/2 + q2, 0}, {1/16, 1}, 1}],
SFAD[{{p1/4 - p2/4 + q1, 0}, {1/16, 1}, 1}]}, {q1, q2}, {p1,
p2}, {Hold[Pair][Momentum[p1, D], Momentum[p1, D]] -> 1,
Hold[Pair][Momentum[p2, D], Momentum[p1, D]] -> 13/10,
Hold[Pair][Momentum[p2, D], Momentum[p2, D]] -> 1}, {}]}}.