Exact results in gauge–string dualities (Stockholm, Sweden, 23 January–17 February 2012)

Abstract

Exactly solvable models play a distinguished role in physics, as they help us understand the behavior of strongly correlated, strongly coupled systems in the regimes where other methods fail. For a long time, the exact solvability was associated with (1+1)-dimensional systems, where powerful methods of integrability allow one to find the exact spectrum, to study thermodynamics and to compute correlation functions for a number of strongly interacting field theories. The AdS/CFT duality established a rigorous relationship between gauge fields and strings, and paved the way for applying the methods of integrability in four-dimensional gauge theories. The two-dimensional dynamics on the string worldsheet (dual to the fluctuating electric flux tube in a gauge theory) is in many cases integrable, which opens the avenue for applications of non-perturbative, integrability-based methods to four-dimensional gauge theories. The progress in understanding non-perturbative phenomena in gauge theories has been rapid in recent years, and required synergy of methods from exactly solvable models, gauge theories, strings and integrable systems. The program 'Exact Results in Gauge–String Dualities' took place at Nordita, Stockholm from 23 January to 17 February 2012 and brought together specialists with common interests in string theory, quantum field theory and exactly solvable models. Topics discussed during the program included: (i) exact results in the AdS/CFT correspondence, (ii) scattering amplitudes, (iii) supersymmetric gauge theories, and (iv) Bethe ansatz and exact solvability in quantum field theory and statistical systems.The articles by D Sorokin [1] and M de Leeuw et al [2] give an overview of the string-theory origins of integrability in gauge theories, and of the algebraic structures omnipresent in quantum integrable systems. The topics covered in these articles underpin the integrability approach to gauge--string dualities and lie at the heart of the integrability-based methods, which are being used to obtain exact non-perturbative results in gauge theories.