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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 12th 2015
• (edited Nov 12th 2015)

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.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeMay 1st 2019

Fixed a couple of typos. But a question too, why does F-theory not have its own kind of branes? Why these degeneration loci? I guess that amounts to why nothing analogous to the M-branes on the left top of this.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 1st 2019
• (edited May 1st 2019)

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).

• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeMay 1st 2019

So one could fill in more of the column headed ’F-theory on elliptically fibered-K3 fibration’ in this table?

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMay 1st 2019
• (edited May 1st 2019)

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!

• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeMay 2nd 2019

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’.

• CommentRowNumber7.
• CommentAuthorDavid_Corfield
• CommentTimeMay 2nd 2019

Put in those dittos.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeMay 2nd 2019

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.