There is a deep connection between the U-duality groups of M-theory and the embedding of the 11-dimensions in the extended superspace which under the gauge and diffeomorphism group actions, induces a continuous symmetry. Here, I will relate the F-theory action to that of M-theory in the context of the F-theory/M-theory duality with an representation. Recall that F-theory is a one-time theory, so let us start with how to make a space-like brane time-like in M-theory. Keeping in mind that the total action of M-theory is given by:

as I showed here, with the D-p-brane world-volume tension, and the Yang-Mills field strength being:

and by a Paton-Chern-Simons factor, we get:

the instanton field, with:

and .

Space-like branes are a class of time-dependent solutions of M-theory with topological defects localized in (P + 1)-dimensional space-like surfaces and exist at a moment in time, and are time-like super-tachyonic kink solutions of unstable D(P + 1)-branes in string theory and provide the topology of the throat-bulk. Let us start with a Dp-Dp pair Lagrangian, fixing the boundary of the string field theory superspace, so that the action is:

with

and

A Teichmuller BPS D(P+1)-brane 2-D reduction gives us the throat action: