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M-THEORY - 2

But how do these systems fit together? To begin with, it immediately catches the eye that some theories are very similar and can be linked using the T-duality, which allows to cancel the differences between large and small distances by compacting the extra spatial dimensions, like Type IIA with Type IIB and HO with HE. What does this mean? That the mathematical description of a radius R in IIA or HO corresponds to a radius 1/R in IIB or HE. We have already reduced the superstring theories to three: Type I, Type II and heterotic.

Now we must apply the S-duality, which allows merging theories with different coupling constants. Coupling constants are dimensionless quantities that define the intensity of the four fundamental interactions at a given energy level. This duality, therefore, combines Type I with heterotic, since weakly interacting particles in Type I equal to particles with high-intensity interactions in heterotic theories. The subtle link does not wholly satisfy rigorous mathematical criteria, but it still makes clear that these theories are somehow connected. There are therefore still only two superstrings: the heterotic and Type II.

The web of dualities that link the various string theories

However, their unification is the most problematic:

Strings are extremely small and difficult to see (if particles were as big as the Solar System, the string would be the size of a tree)

The quantum theory that describes the lower energy limits does not consider strings, but particles that move in space-time

Since strings also include gravity, at low energy levels, they are expected to correspond to ordinary particles moving in a gravitational field

Supersymmetry should appear in the approximations of the theoretical descriptions of these low-energy states

So, the Superstring Theory becomes a Supergravity Theory, shifting the problem. The link, albeit weak, still seems to exist.

Indeed, if we consider just 10 dimensions, we have only two Supergravity Theories, Type IIA and Type IIB, whose lower energy levels correspond to the homonymous superstrings. Furthermore, since heterotic theories can be reduced to the two Types II due to the lower energy level, the Type IIA Supergravity would also correspond to the heterotic superstrings if it were the result of a dimensional reduction of a single Theory of Supergravity to 11 dimensions. However, at the moment, especially at high energy levels, it generates paradoxical results.

Diagram of string theories unified in the M-Theory

PICS CREDITS

The web of dualities linking superstring theories in D 10 and their embedding in - physics.uu.se/research/theoretical-physics/

M-Theory – Olena Shamahalo