QCD: string theory meets collider physics

13 March 2008

Two fields of physics met at the 2007 DESY theory workshop

With the title Quantum Chromodynamics – String Theory meets Collider Physics, the 2007 DESY theory workshop brought together a distinguished list of speakers to present and discuss recent advances and novel ideas in both fields. Among them was Juan Maldacena from the Institute for Advanced Study, Princeton, pioneer of the interrelationship between gauge theory and string theory, who also gave the Heinrich Hertz lecture for the general public.


From a dynamical point of view, quantum chromodynamics (QCD), the theory of strong interactions, represents the most difficult sector of the Standard Model. Mastering the complexities of strong interactions is essential for a successful search for new physics at the LHC. In addition, the relevance of the QCD phase transition for the early evolution of our universe has ignited an intense interest in heavy-ion collisions, both at RHIC in Brookhaven and at the LHC at CERN. The QCD community is thus deeply engaged in investigations to further our understanding of QCD, to reach the highest accuracy in its theoretical predictions and to advance existing computational tools.


String theory, initially considered a promising theoretical model for strong interactions, was long believed incapable of capturing, in detail, the correct high-energy behaviour. In 1997, however, Maldacena overcame a prominent obstacle for applications of string theory to gauge physics. He proposed describing strongly coupled four-dimensional (supersymmetric) gauge theories through closed strings in a carefully chosen five-dimensional background. In fact, equivalences (dualities in modern parlance) between gauge and string theories emerge, provided that the strings propagate in a five-dimensional space of constant negative curvature. Such a geometry is called an anti deSitter (AdS) space and the duality involving strings in an AdS background became known as AdS/CFT correspondence, where CFT denotes conformal field theory. If the duality turns out to be true, string-theory techniques can give access to strongly coupled gauge physics, a regime that only lattice gauge theory has so far been able to access. Though a string theory dual to real QCD has still to be found, AdS/CFT dualities are beginning to bring string theory closer to the “real world” of particle physics.

With the duality conjecture as its focus, the DESY workshop covered the full spectrum of research topics that have entered this interdisciplinary endeavour. Topics ranged from the role of QCD in the evaluation of experimental data and in Monte Carlo simulations to string theory calculations in AdS spaces.

To begin with the more practical side, QCD clearly dominates the daily analysis of data from RHIC, HERA at DESY, and Fermilab’s Tevatron. Tom LeCompte of Argonne presented results from the Tevatron, and Uta Klein of Liverpool looked at what we have learned from HERA. The results relating to parton densities will be of utmost importance for measurements at the LHC, not least in the kinematic region of small x, which was among the highlights of HERA physics. Diffraction – one of the puzzles for the HERA community – continues to demand attention at the LHC, in particular as a clean channel for the discovery of new physics, as Brian Cox of the University of Manchester explained.

Monte Carlo simulations represent an indispensable tool for analysing experimental data, and existing models need steady improvement as we approach the new energy regime at the LHC. Gösta Gustafson of Lund and Stefan Gieseke of Karlsruhe described the progress that is being made in this respect. Topics of particular current interest include a careful treatment of multiple parton interactions and the implementation of next-to-leading-order (NLO) QCD matrix elements in Monte Carlo programs.

At present, lattice calculations still offer the most reliable framework for studies of QCD beyond the weak coupling limit. Among other issues, the workshop addressed the calculation of low-energy parameters such as hadron masses and decay constants. In this context, Federico Farchioni of Münster noted that the limit of small quark masses calls for careful attention, and Philipp Hägler of Technische Universität, München discussed developments in calculating hadron structure from the lattice. Another important direction concerns the QCD phase structure and, in particular, accurate estimates of the phase-transition temperature, Tc, as Akira Ukawa of Tsukuba explained. Lattice gauge theories also allow the investigation of connections with string theory. Michael Teper of Oxford showed how once the dependence of gauge theory on the number of colours, Nc, is sufficiently well controlled, it may be possible to determine the energy spectrum of closed strings in the limit of large ‘t Hooft coupling.

QCD perturbation theory

NLO and next-to-NLO calculations in QCD perturbation theory are needed to derive precise expressions for cross-sections – they are crucial in describing experimental data at the existing colliders, and indispensable input for the discrimination of new physics from mere QCD background at the LHC. The necessary computations require a detailed understanding of perturbative QCD, as Werner Vogelsang from Brookhaven National Laboratory discussed. For example, the theoretical foundation of kt factorization and of unintegrated parton densities, along with their use in hadron–hadron collisions, is attracting much attention. For higher-order QCD calculations, Alexander Mitov of DESY, Zeuthen, described how advanced algorithms are being developed and applied.

Higher-order computations in QCD are becoming one of the most prominent examples of an extremely profitable bridge between gauge and string theories. Multiparton final states at the LHC have sparked interest in perturbative gauge theory computations of scattering amplitudes that involve a large number of incoming and/or outgoing partons. At the same time there is an urgent need for higher-loop results, which, in view of the rapidly growing number of Feynman diagrams, seem to be out of reach for more conventional approaches. Recent investigations in this direction have unravelled new structures, such as in the perturbative expansion of multigluon amplitudes.

In a few special cases, such as four-gluon amplitudes in N = 4 supersymmetric Yang–Mills theory, these investigations have led to highly non-trivial conjectures for all loop expressions. This was the topic of talks by David Dunbar of Swansea and Lance Dixon of Stanford. According to the AdS/CFT duality, the strong coupling behaviour of these amplitudes should be calculable within string theory. Indeed, Maldacena described how the relevant string-theory computation of four-gluon amplitudes has been performed, yielding results that agree with the gauge theoretic prediction. On the gauge theory side, a conjecture for a larger number of gluons has also been formulated. Maldacena noted that this is currently contested both by string theoretic arguments and more refined gauge theory calculations.

The expressions for four-gluon amplitudes contain a certain universal function, the so-called cusp anomalous dimension, which can again be computed at weak (gauge theory) and strong (supergravity) coupling. Gleb Arutyunov of Utrecht showed how this particular quantity is also being investigated using modern techniques of integrable systems. Remarkably, as Niklas Beisert of the Albert Einstein Institute in Golm explained, a formula for the cusp anomalous dimension in N = 4 super-Yang–Mills theory has recently been proposed that interpolates correctly between the known weak and strong coupling expansions. In addition, Vladimir Braun of Regensburg and Lev Lipatov of Hamburg and St Petersburg described how integrability features in the high-energy regime of QCD, both in the short distance and the small-x limit. The integrable structures have immediate applications to data analysis. Yuri Kovchegov of Ohio also pointed out that low-x physics in QCD, with all the complexities appearing in the NLO corrections, might possess close connections with the supersymmetric relatives of QCD. The higher order generalization of the Balitsky–Fadin–Kuraev–Lipatov pomeron, which is expected to correspond to the graviton, is of particular interest. In this way, studies of the high-energy regime seem to carry the seeds for new relations to string theory.

Another close contact between string theory and QCD appears at temperatures near and above the QCD phase transition. Heavy-ion experiments that probe this kinematic region are currently taking place at RHIC and will soon be carried out at the LHC. CERN’s Urs Wiedemann introduced the topic, and John Harris of Yale presented results and discussed their interpretation. The analysis of RHIC data requires somewhat unusual theoretical concepts, including, for example, QCD hydrodynamics. As in any other system of fluid mechanics, viscosity is an important parameter used to characterize quark–gluon plasmas, but its measured value cannot be explained through perturbative QCD. This suggests that the quark–gluon plasma at RHIC is strongly coupled, so string theory should be able to predict properties such as the plasma’s viscosity through the AdS/CFT correspondence. David Mateos of Santa Barbara and Hong Liu of Boston showed that the string theoretic computation of viscosity and other quantities is indeed possible, based on investigations of gravity in a thermal black-hole background. It leads to values that are intriguingly close to experimental data.

String theory is often perceived as an abstract theoretical framework, far away from the physics of the real world and experimental verification. When considered as a theory of strongly coupled gauge physics, however, it is beginning to slip into a new role – one that offers novel views of qualitative features of gauge theory and, in some cases, even quantitative predictions. The QCD community, on the other hand, is beginning to realize that its own tremendous efforts may profit from the novel alliance with string theory. The participants of the 2007 DESY Theory workshop witnessed this recent shift, through lively discussions and numerous excellent talks that successfully bridged the two communities.

bright-rec iop pub iop-science physcis connect