String bits in small radius AdS and weakly coupled N=4 Super Yang-Mills Theory: I

Details String bits in small radius AdS and weakly coupled N=4 Super Yang-Mills Theory: I String bits in small radius AdS and weakly coupled N=4 Super Yang-Mills Theory: I

2003-04-07

arxiv.org/abs/hep-th/0304062v2

Physics

High Energy Physics

High Energy Physics - Theory

35 pages; (v2)problems in taking the continuum limit highlighted, the section on AdS/CFT matching rewritten in the light of th

Scientific paper

We study light-cone gauge quantization of IIB strings in AdS_5 \times S^5 for small radius in Poincare coordinates. A picture of strings made up of noninteracting bits emerges in the zero radius limit. In this limit, each bit behaves like a superparticle moving in the AdS_5 \times S^5 background, carrying appropriate representations of the super conformal group PSU(2,2|4). The standard Hamiltonian operator which causes evolution in the light-cone time has continuous eigenvalues and provides a basis of states which is not suitable for comparing with the dual super Yang-Mills theory. However, there exist operators in the light-cone gauge which have discrete spectra and can be used to label the states. We obtain the spectrum of single bit states and construct multi-bit states in this basis. There are difficulties in the construction of string states from the multi-bit states, which we discuss. A non-zero value of the radius introduces interactions between the bits and the spectrum of multi-bit states gets modified. We compute the leading perturbative corrections at small radius for a few simple cases. Potential divergences in the perturbative corrections, arising from strings near the boundary, cancel. This encourages us to believe that our perturbative treatment could provide a framework for a rigorous and detailed testing of the AdS/CFT conjecture, once the difficulties in the construction of string states are resolved.

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