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I have created a table-for-inclusion that means to list how all the M-branes transmute into all the “F-branes”, i.e. all the superstrings, D-branes and N5-branes.
Then I have included this table into some of the relevant entries.
At least the last column (duality to heterotic string theory) still needs to be filled in more.
One wouldn’t say that F-theory does not have “it’s own branes”. Just as in M-theory, some of the objects that appear as branes in 10d string theory become “geometrized” in F-theory, notably those 7-branes (corresponding to the geometrization of 6-branes in M-theory).
So one could fill in more of the column headed ’F-theory on elliptically fibered-K3 fibration’ in this table?
Oh, now I see what your question is. Yes, all those empty boxes in the F-theory column are really to be thought as filled with the same content of the type IIB box to the left of them.
I am on my phone now and won’t edit, but if you have a minute you could put "
in each of these boxes. Thanks!
Can anything be included as a column between the Type IIB column and the F-theory column as there is ’KK-compactification’ between M-theory and Type IIA. I know vaguely the relationship isn’t the same:
This is a hypothetical or rather auxiliary twelve dimensional theory which, when compactified on a two-dimensional torus, gives the Type IIB superstring… However, this twelve-dimensional interpretation is not meant in the sense of a standard Kaluza-Klein reduction… Hence the 12-dimensional interpretation serves just to provide a geometrization of the Type IIB $SL(2, \mathbb{Z})$ duality symmetry rather than to correspond to a real compactification from twelve to ten dimensions (Blumenhagen 10)
Elsewhere at F-theory we label this relation ’axio-dilaton is modulus of elliptic fibration’.
Thanks!
Right, for being more systematic the table could well give a name for that transition from IIB to F. It’s to be called something like “geometrize the axio-dilaton”.
That doesn’t capture it completely, as in addition to geometrizing the coupling constant, F-theory then allows it to be large, but maybe it would be close enough for the purpose of a survey table.
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