String solitons

Abstract

We review the status of solitons in superstring theory, with a view to understanding the strong coupling regime. These solitonic solutions are non-singular field configurations which solve the empty-space low-energy field equations (generalized, whenever possible, to all orders in α ′ ), carry a non-vanishing topological "magnetic" charge and are stabilized by a topological conservation law. They are compared and contrasted with the elementary solutions which are singular solutions of the field equations with a σ-model source term and carry a non-vanishing Noether "electric" charge. In both cases, the solutions of most interest are those which preserve half the spacetime supersymmetries and saturate a Bogomol'nyi bound. They typically arise as the extreme mass=charge limit of more general two-parameter solutions with event horizons. We also describe the theory dual to the fundamental string for which the roles of elementary and soliton solutions are interchanged. In ten spacetime dimensions, this dual theory is a superfivebrane and this gives rise to a string/fivebrane duality conjecture according to which the fivebrane may be regarded as fundamental in its own right, with the strongly coupled string corresponding to the weakly coupled fivebrane and vice-versa. After compactification to four spacetime dimensions, the fivebrane appears as a magnetic monopole or a dual string according as it wraps around five or four of the compactified dimensions. This gives rise to a four-dimensional string/string duality conjecture which subsumes a Montonen-Olive type duality in that the magnetic monopoles of the fundamental string correspond to the electric winding states of the dual string. This leads to a duality of dualities whereby under string/string duality the strong/weak coupling S-duality trades places with the minimum/maximum length Tduality. Since these magnetic monopoles are extreme black holes, a prediction of S-duality is that the corresponding electric massive states of the fundamental string are also extreme black holes. This is indeed the case.

Curvatures and potential of M–theory inD= 4 with fluxes and twist

“…Higher dimensional theories of supergravity include (p + 1)-form gauge fields which may couple to p-branes, as well as (D − 3 − p)-form magnetic potentials which have "magnetic" (D − 4 − p)-branes as sources (for a review see [1]). When these theories are compactified to lower-dimensions, S and T -dualities, as well as extended supersymmetry, give rise to noncompact global symmetries [3] called U-dualities [4].…”

“…Equation (4.4) implies that its right hand side is a closed form. In fact the crucial ingredient is that the term F (1) IJK F (0) P QRS ǫ IJKP QRS is an exact form on the twisted torus with fluxes, and it can be written as…”

Structure of composite black p-brane configurations and related black holes

“…1 Some special cases were discussed, e.g., in [8,5,9,10,11,12] (see [6] for a more complete list of references).…”

“…Further T -dualities [17] generate various black R-R p-brane backgrounds [8], in particular, the 5-brane of type IIB theory. Applying the SL(2) duality then leads to the solitonic NS-NS 5-brane, thus effectively performing the 'electro-magnetic' duality transformation between the fundamental string and the solitonic 5-brane [9]. The D = 10 black 2-brane and 5-brane backgrounds can then be lifted to D = 11, thus explaining the structure of the resulting non-extremal D = 11 solutions [5] in terms of (4) and lower-dimensional dualities.…”

“…Compactification then leads to the three-charge D = 5 black hole. 9 Notice that one never needs to decide which combinations of branes are possible -they are automatically selected by the duality transformations. 10 As the duality transformations preserve supersymmetry of the extremal solutions, one may say that the origin of the 1/2 supersymmetry of the single branes (or non-threshold bound states related to some of them by SL(2) rotations) is in supersymmetry of a wave or T -dual fundamental string background, while the reason for the 1/4 supersymmetry of the threshold combinations of two branes is in the 1/4 supersymmetry of the fundamental string with momentum, etc.…”