Advances in Theoretical and Mathematical Physics

Volume 15 (2011)

Number 4

Perturbative study of the transfer matrix on the string worldsheet in ${\rm AdS}^5 \times S_5$

Pages: 913 – 971

DOI: http://dx.doi.org/10.4310/ATMP.2011.v15.n4.a1

Authors

Andrei Mikhailov

Sakura Schäfer-Nameki

Abstract

Quantum non-local charges are central to the quantum integrability of a sigma model. In this paper we study the quantum consistency and UV finiteness of non-local charges of string theory in ${\rm AdS}^5 \times S_5$. We use the pure spinor formalism. We develop the near-flat space expansion of the transfer matrix and calculate the one-loop divergences. We find that the logarithmic divergences cancel at the level of one loop. This gives strong support to the quantum integrability of the full string theory. We develop a calculational setup for the renormalization group analysis of Wilson line type of operators on the string worldsheet.

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