One-loop free energy of tensionless type IIB string in AdS$_5\times$S$^5$

Abstract : Considering the zero ’t Hooft coupling limit of $ \mathcal{N}=4 $ super-Yang-Mills theory, the exact spectrum of all single-trace operators can be accessed in terms of the underlying so(2, 4) character. This makes it possible in turn to compute the one-loop free energy of the tensionless type IIB string theory in AdS$_{5}$×S$^{5}$ background, with help of the recently developed method of character integral representation of zeta function (CIRZ). We calcu-late first the one-loop free energy of the string states in the (p − 1)-th Regge trajectory and find the result to be p times the free energy of a single $ \mathcal{N}=4 $ Maxwell multiplet. The full one-loop free energy is hence proportional to the divergent series $ {\displaystyle {\sum}_{p=2}^{{\infty }}p} $ . The divergence arises as a result of interrupting the regularization procedure in an intermediate stage. With a reorganization of states, we extract the finite part of free energy after summing over the Regge trajectories. This way gives us a finite result which is minus of the free energy of the $ \mathcal{N}=4 $ multiplet. Hence, this bulk one-loop result matches the −1 term in the N$^{2}$ − 1 factor of the boundary result.
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JHEP, 2017, 1706, pp.155. <10.1007/JHEP06(2017)155>
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Soumis le : mercredi 6 septembre 2017 - 13:52:39
Dernière modification le : samedi 9 septembre 2017 - 03:23:48

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Jin-Beom Bae, Euihun Joung, Shailesh Lal. One-loop free energy of tensionless type IIB string in AdS$_5\times$S$^5$. JHEP, 2017, 1706, pp.155. <10.1007/JHEP06(2017)155>. <hal-01582878>

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