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 AdS5×S5 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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Bae, JB., Joung, E. & Lal, S. One-loop free energy of tensionless type IIB string in AdS5×S5 . J. High Energ. Phys. 2017, 155 (2017). https://doi.org/10.1007/JHEP06(2017)155
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DOI: https://doi.org/10.1007/JHEP06(2017)155