One-loop free energy of tensionless type IIB string in AdS5×S5

• Main Authors: Jin-Beom Bae, Euihun Joung, Shailesh Lal
• Format: Article
• Language: English
• Published: SpringerOpen 2017-06-01
• Series: Journal of High Energy Physics
• Subjects: 1/N Expansion; AdS-CFT Correspondence; Higher Spin Gravity; Higher Spin Symmetry
• Online Access: http://link.springer.com/article/10.1007/JHEP06(2017)155

Abstract Considering the zero ’t Hooft coupling limit of N = 4 $$ \mathcal{N}=4 $$ 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 N = 4 $$ \mathcal{N}=4 $$ Maxwell multiplet. The full one-loop free energy is hence proportional to the divergent series ∑ p = 2 ∞ p $$ {\displaystyle {\sum}_{p=2}^{{}_{\infty }}p} $$ . 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 N = 4 $$ \mathcal{N}=4 $$ multiplet. Hence, this bulk one-loop result matches the −1 term in the N 2 − 1 factor of the boundary result.