Quantum strings in AdS_5 x S^5: strong-coupling corrections to dimension of Konishi operator

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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33 pages, Latex v2: minor comments added, misprints corrected v3: misprint corrected v4: misprints corrected

Scientific paper

10.1088/1126-6708/2009/11/013

We consider leading strong coupling corrections to the energy of the lightest massive string modes in AdS_5 x S^5, which should be dual to members of the Konishi operator multiplet in N=4 SYM theory. This determines the general structure of the strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for several semiclassical string states to extract information about the leading coefficients in this expansion. Our prediction is Delta= 2 lambda^{1/4} + b_0 + b_1 lambda^{-1/4} + b_3 lambda^{-3/4} +..., where b_0 and b_1 are rational while b_3 is transcendental containing zeta(3). Explicitly, we argue that b_0= Delta_0 - 4 (where Delta_0 is the canonical dimension of the corresponding gauge-theory operator in the Konishi multiplet) and b_1=1. Our conclusions are sensitive to few assumptions, implied by a correspondence with flat-space expressions, on how to translate semiclassical quantization results into predictions for the exact quantum string spectrum.

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