# 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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Article dans une revue
JHEP, 2017, 06, pp.155. 〈10.1007/JHEP06(2017)155〉

https://hal.archives-ouvertes.fr/hal-01582878
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Soumis le : mercredi 6 septembre 2017 - 13:52:39
Dernière modification le : mardi 13 février 2018 - 01:30:47

### Citation

Jin-Beom Bae, Euihun Joung, Shailesh Lal. One-loop free energy of tensionless type IIB string in AdS$_5\times$S$^5$. JHEP, 2017, 06, pp.155. 〈10.1007/JHEP06(2017)155〉. 〈hal-01582878〉

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