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\(AdS_{4}/CFT_{3}\) at one loop. (English) Zbl 1245.81197

Summary: We consider semi-classical type IIA strings rotating in the \(\mathrm{AdS}_4\) part of \(\mathrm{AdS}_4\times\mathbb C\mathbb P^3\). The one-loop sigma model corrections to this classical solution are used to compute the energy shift, and the result is found to be \(E-S=f(\lambda)\ln S\) with \(f(\lambda)=\sqrt{2\lambda}-\frac{5\ln 2}{2\pi}+ O(\frac{1}{\sqrt\lambda})\). Even though the functional forms match, the actual numerical value of this one-loop string result differs from the result obtained on the integrable \(\mathcal N=6\) Chern-Simons (ABJM) theory side.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory

Keywords:

QCD; bulk viscosity