## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 15, Number 4 (2011), 913-971.

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

Andrei Mikhailov and 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.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 15, Number 4 (2011), 913-971.

**Dates**

First available in Project Euclid: 11 June 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1339438348

**Mathematical Reviews number (MathSciNet)**

MR2929679

**Zentralblatt MATH identifier**

1253.81111

#### Citation

Mikhailov, Andrei; Schäfer-Nameki, Sakura. Perturbative study of the transfer matrix on the string worldsheet in ${\rm AdS}^5 \times S_5$. Adv. Theor. Math. Phys. 15 (2011), no. 4, 913--971. https://projecteuclid.org/euclid.atmp/1339438348