In the Shortest Superstring problem (SS) one has to find a shortest string s containing given strings s1, . . . , sn as substrings. The problem is NP-hard, so a natural question is that of its approximability. One natural approach to approximately solving SS is the following GREEDY heuristic: repeatedly merge two strings with the largest overlap until only a single string is left. This heuristi...

This is a short review of superstring theories, highlighting the important concepts, developments and open problems of the subject.

Nathan Berkovits Instituto de F sica Te orica, Univ. Estadual Paulista Rua Pamplona 145, S~ao Paulo, SP 01405-900, BRASIL e-mail: [email protected] The free action for the massless sector of the Type II superstring was recently constructed using closed RNS superstring eld theory. The supersymmetry transformations of this action are shown to satisfy an N=2 D=10 SUSY algebra with Ramond-Ramon...

A large class of equivalence relations between the moduli spaces of instantons on ALE spaces and the Higgs branches of supersymmetric Yang-Mills theories, are found by means of a certain kind of duality transformation between brane configurations in superstring theories. 4d, N=2 and 5d, N=1 supersymmetric gauge theories with product gauge groups turn out to correspond to the ALE-instanton modul...

A geometrical formulation of the T-duality rules for type II superstring Ramond–Ramond fields is presented. This is used to derive the Wess-Zumino terms in superstring D-brane actions, including terms proportional to the mass parameter of the IIA theory, thereby completing partial results in the literature. For non-abelian world-volume gauge groups the massive type IIA D-brane actions contain n...

In this paper we perform the calculation of the gravitational scattering amplitude for 4 massless scalars in quantum field theory and Type II superstring theory. We show that the results agree, providing an example of how gravity is incorporated in the superstring theory. During the calculation we quantize gravitational action to derive graviton propagator and interaction vertex with massless s...

Exploiting the fact that Kaluza–Klein monopoles and the associated generalized orbifold planes are sources for geometrical fluxes, ω, we show that the standard constraint ω ω = 0, valid for superstring compactifications on twisted tori, can be consistently relaxed. This leads to novel possibilities for constructing superstring models with fluxes and localized sources, as well as for stabilizing...