String theory offers a number of insights into the theory of strong interactions. The quantum states of a rotating open string have key properties of hadronic excitations. The energy of a stretched string matches quite well the potential energy of a separated quark–antiquark pair. More surprisingly, certain strongly interacting gauge theories are physically equivalent to closed string theories. The closed strings propagate on a space whose boundary is roughly the space where the gauge theory lives. The prime example of this equivalence is the AdS/CFT correspondence, which states that supersymmetric four-dimensional SU(N) gauge theory is fully described by type IIB closed superstrings in a spacetime that includes the five-dimensional anti-de Sitter space AdS5. We motivate this correspondence and examine in detail the geometry of anti-de Sitter space and related hyperbolic spaces. The correspondence suggests that properties of the recently discovered quark–gluon plasma are related to properties of black holes in anti-de Sitter space.
Introduction
String theory was discovered in the attempts to understand the dynamics of strongly interacting hadrons. It had been noted that the plot of the angular momentum J of hadronic excitations against their energy-squared falls roughly into lines J = α′E2 called Regge trajectories. String theory seemed to be a reasonable candidate for a theory of strong interactions because this relationship between J and E2 emerges naturally from a rotating classical open string, as we discussed in Section 8.6.
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