String Theory and M-Theory

332 M-theory and string duality
M-branes
The BPS branes of M-theory are the M2-brane and the M5-brane. M-theory
on ¡ 11 does not contain any strings. This raises the following question:
What happens to the type IIA fundamental string for large coupling, when
the theory turns into M-theory? The only plausible guess is that the type
IIA F-string is actually an M2-brane with a circular dimension wrapping
the circular eleventh dimension. Since tension is energy density, this identification
requires that
This relation is satisfied by the tensions
TF1 = 1
2πℓ 2 s
TF1 = 2πR11TM2. (8.107)
and TM2 = 2π
, (8.108)
(2πℓp) 3
as can be verified using R11 = ℓsgs and ℓp = g 1/3
s ℓs. All of these relations
were presented earlier, and the proposal presented here confirms that they
are correct. Various other branes can be matched in a similar manner. For
example, the D4-brane is identified to be an M5-brane with one dimension
wrapped on the spatial circle.
Another interesting fact can be deduced by considering the M-theory origin
of a type IIA configuration in which an F-string ends on a D4-brane.
In view of the above, this clearly corresponds to an M2-brane ending on
an M5-brane, where each of the M-branes is wrapped around the circular
dimension. One reason that a type IIA F-string can end on a D-brane is
that the flux associated with the charge at the end of the string is carried
away by the one-form gauge field of the D-brane world-volume theory. That
being the case, one can ask what is the corresponding mechanism for Mbranes.
The end of the M2-brane is a string inside the M5-brane. So the
world-volume theory of the M5-brane must contain a two-form gauge field
A2 to carry away the associated flux. That is indeed the case. In fact,
the corresponding field strength F3 is self-dual, just like the five-form field
strength in type IIB supergravity.
The D6-brane
The preceding discussion explained the M-theory origin of the type IIA Dpbranes
for p = 0, 2, 4 in terms of wrapped or unwrapped M-branes. This
raises the question of how one should understand the D6-brane from an
M-theory point of view. Clearly, unlike the other D-branes, it cannot be
related to the M2-brane or the M5-brane in any simple way. The key to