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

Abstract

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.

35 pages; (v2)problems in taking the continuum limit highlighted, the section on AdS/CFT matching rewritten in the light of these problems, typos corrected and references added; the main conclusion about finiteness of the small radius expansion unchanged

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Cited by in corpus (26)

• On stringy AdS_5 x S^5 and higher spin holography
• From Free Fields to $AdS$
• Higher Spin Symmetry and N=4 SYM
• On the Frame-Like Formulation of Mixed-Symmetry Massless Fields in (A)dS(d)
• From Free Fields to $AdS$ -- III
• Structure constants of planar N =4 Yang Mills at one loop
• Brane Partons and Singleton Strings
• Quantum AdS_5 x S^5 superstring in the AdS light-cone gauge
• Towards a string bit formulation of N=4 super Yang-Mills
• The Worldsheet Dual of Free Super Yang-Mills in 4D
• Construction of bosonic string theory on infinitely curved Anti-de Sitter space
• Spin bit models from non-planar N=4 SYM
• Comments on worldsheet theories dual to free large N gauge theories
• On a worldsheet dual of the Gaussian matrix model
• From Spacetime to Worldsheet: Four point correlators
• From Free Fields to AdS -- Thermal Case
• Positive Energy Unitary Irreducible Representations of the Superalgebras osp(1|2n,R)
• String bits without doubling
• Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry
• Large N limit of SYM theories with 16 supercharges from superstrings on Dp-brane backgrounds
• Conifold Holography
• Quantum fluctuations of rotating strings in AdS_5 x S^5
• Spacetime Virasoro algebra from strings on zero radius AdS_3
• Physical Fock space of tensionless strings
• Strings on Plane Waves and AdS x S
• Covariant Hamiltonian evolution in supersymmetric quantum systems