The quest for understanding strong interactions has a long history. The challenge to construct a fundamental theory of the interactions which bind together protons and neutrons in atomic nuclei, and which are responsible for hundreds of hadronic resonances, led to the advent and development of theoretical methods which later found applications in many fields of physics. The list includes powerful tools such as the renormalization group, lattice field theory, and effective field theories. One line of such theoretical developments brought about in the course of this quest lead to the Regge phenomenology of hadrons and the Veneziano amplitude, culminating in the discovery of string theory. It is a well-known fact that string theory emerged as a candidate for the theory of strong interactions before the advent of QCD.

The discovery of asymptotic freedom, followed by many impressive phenomenological successes, firmly established QCD as the fundamental theory of strong interactions. Soon after, string theory metamorphosed into a theory of quantum gravity. Nevertheless, the connection between string theory and strong interactions has never been completely lost—the existence of QCD flux tubes and the planar diagram dominance in large-Nc QCD hinted that string theory might still be a needed mathematical tool for understanding confinement. The strong coupling regime of QCD has always remained a challenge to analytical first-principle QCD approaches, and it has long been clear that qualitatively new methods and ideas are necessary to treat such non-perturbative phenomena as confinement and chiral symmetry breaking, and to understand the hadron spectra and interactions.

The modern period of exploration of the QCD/string connection started with the formulation of the conjecture of gauge/string duality, or AdS/CFT correspondence, in 1997–98 by Maldacena and others. A weaker form of the conjecture is the gauge/gravity correspondence, which makes use of only some features of the string theory. This correspondence allows one to solve many problems in a class of strongly coupled gauge theories, including some QCD-like theories. In principle, gauge/gravity duality should apply to asymptotically free theories like QCD. In practice, however, no rigorous calculational methods for such theories are known.

Despite this drawback, the methods of gauge/gravity duality have recently become very popular among QCD practitioners. The power of these methods is that they are ideally suited for the strongly interacting regime. Moreover, the string methods could be applied where the traditional “brick and mortar” numerical lattice approach is not effective, such as, e.g., non-equilibrium and real-time dynamics. The purpose of the INT program “From Strings to Things” was to further the development of these novel methods and bring them to bear on most pressing problems in QCD and strong interactions. This is the second time a meeting dedicated to string theory methods has taken place at the INT: a four-day workshop “QCD and String Theory” was held at the INT in February 2002.

During the program “From Strings to Things” , one of the most actively discussed applications of string theory methods was to describe the real-time dynamics of strongly coupled quantum field theories at high temperature and density. The major discovery of RHIC experiments is that the matter created in heavy ion collisions at RHIC is not a weakly interacting plasma of quarks and gluons (QGP) but rather a strongly interacting medium (sQGP), which defies traditional kinetic description in terms of well-defined quasiparticles. How does this medium expand and cool? What happens when a very energetic quark or gluon, occasionally created in the initial stages of the collision, traverses this medium? How and on what time scales does thermalization occur? Can quarks coalesce into hadrons inside such a medium and under what conditions? These and many other important and intriguing questions need answers from QCD, and yet in the strong coupling regime the necessary mathematical apparatus is lacking. AdS/CFT methods allow one to study these questions and obtain reliable answers in theories which share many of the QCD properties, and which are strongly interacting.

Fig 1:The wake of a quark moving with supersonic velocity in the N=4 super-Yang-Mills plasma. It is hoped that the properties of this plasma is not too different from the quark-gluon plasma created at RHIC (source: Paul Chesler's talk at the program).

It is remarkable that the developments of the string theory applications to hot and dense matter go hand-in-hand with current heavy-ion collision experiments at RHIC. One of the goals of the four-day mini-workshop embedded into this INT program was to bring together theorists and experimentalists in order to increase theorists' appreciation of experimental challenges as well as experimentalists' understanding of the potential and limitations of the string theory methods.

Another active avenue of research is the development of models which go beyond the original AdS/CFT correspondence by incorporating such features of QCD as confinement and chiral symmetry breaking—AdS/QCD models or holographic QCD. Two complementary approaches have emerged. The top-down approach uses the original AdS/CFT setup as a starting point, removes supersymmetry by modifying the background geometry and builds in quarks by introducing additional extended objects (branes). A complementary, bottom-up approach starts from QCD and attempts to build the model which matches relevant QCD correlation functions by using the rules of the holographic correspondence in reverse. One of the distinctive automatic features of these models is the natural matching between sums over resonances and the parton-model behavior of correlation functions. Another important feature is a natural explanation of vector meson dominance. Such models, even in their barest form, enjoy considerable phenomenological success. The most recent developments have been reported and discussed during the INT program such as phenomenology of the baryons (spectra, form factors), the finite density and temperature properties (phase diagrams), the response to external electric and magnetic fields.

Fig. 2: A comparision of the experimental data on the pion form factor with the prediction of various AdS/QCD models. AdS/QCD models work surprisingly well for many low-energy quantities (source: Anatoly Radyushkin's talk at the program).

Many other issues have been also discussed during the program, such as description of hard-scattering in QCD, formal issues such as integrability of N=4 super-Yang-Mills theory, the challenges of going beyond the gravity approximation in AdS/CFT, entanglement entropy, etc. In addition, possible applications of gauge/gravity duality to condensed matter physics have taken shape in the past couple of years; some results in this direction have been reported and actively discussed at the program.

The application of string theory methods to strong interactions is a fast developing subject. The INT program summarized the recent developments, outlined short- and long-term challenges and provided a fruitful ground for exchange of ideas.

Further reading:

1. N. Evans, String theory meets QCD, Physics World, May 2003 issue.
2. J. Maldacena, Into the fifth dimension, Nature 432, 695 (2003).
3. D. T. Son, Liquid Universe hints at strings, Physics World, June 2005 issue.
4. M. Natsuume, Where string theory meets reality? Nature Phys. 3, 297 (2007).
5. J. Zaanen, A black hole full of answers, Nature 488, 1000 (2007).