Gravity and Strings

19
The extended objects of string theory
After the general introduction to extended objects of the preceding chapter, in this one
we are going to study specifically the extended objects that appear in string theory. The
existence of these objects is implied by our previous knowledge of existing objects (strings
and Dp-branes) combined with duality. This path will be followed in Section 19.1, in which
we will arrive at the diagrams in Figures 19.4.1 and 19.4.1 that represent, respectively,
more- and less-conventional extended string/M-theory objects and their duality relations.
The duality relations can be used to find the masses of all these objects compactified on tori
(Tables 19.1–19.3) using as input the mass of a string wound once on a circle (i.e. the mass
of a winding mode). To obtain consistent results (in particular for electric–magnetic dual
branes to coexist satisfying the Dirac quantization condition), the ten-dimensional Newton
constant has to have a specific value in terms of the string coupling constant and the string
length that we will determine.
The next step (Section 19.2) will be to identify which are, among the general solutions
of the p-brane a-model, those that represent the long-range fields of the basic extended
objects of string and M theory that we found before. We will first identify families of
solutions and then we will study one by one the most important solutions. In Section 19.3
we will check the values of the integration constants of those solutions against the masses
and charges of the extended objects that we determined using duality arguments. Then, the
duality relations between the solutions will be checked in Section 19.4.
Next, in Section 19.5 we will learn how a great deal of information about all these objects
is encoded in the spacetime superalgebras of the effective (supergravity) theories. In
particular, the superalgebras tell us (up to a point) which extended objects may exist and the
amount of unbroken supersymmetry preserved by each of them (always half of the total),
as we will check by solving explicitly the Killing-spinor equations (Section 19.5.1).
In Section 19.6 we will study the possible intersections between several of these objects.
The worldvolume fields of the extended objects contain a large amount of information
about these intersections and we will briefly review the worldvolume theories of the extended
objects of string/M theory first. We will construct solutions describing the simplest
intersections, which will be used in Chapter 20 to construct four-dimensional BH solutions.
Some general references with emphasis on p-brane solutions of the string/M-theory effective
actions are [333, 337, 417, 858, 862, 863, 901, 966]. The standard general refer-
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