Department of Physics
UCLA
Los Angeles, CA 90095-1547
e-mail: bern@physics.ucla.edu
phone: (310) 825-8528
fax: (310) 206-5668
In order to find the new physics at particle colliders we need to find discrepancies between data and the known physical laws. An important ingredient in understanding particle collisions are calculations in perturbative quantum chromodymamics (QCD). Such calculations turn out to be rather difficult. I have spent a substantial fraction of my time developing the necessary tools and calculating amplitudes, which will be needed to properly interpret forthcoming data on high multiplicity events at the CERN Large Hadron Collider. Our approach involves replacing Feynman diagrams with what is known as the unitarity method. Some recent inspiration due to Edward Witten from twistor string theory stimulated a number of important new ideas in this area, leading to greatly improved calculational methods. My recent work on multi-particle amplitudes in QCD has been in collaboration with Carola Berger, Lance Dixon, Darren Forde and David Kosower as well as with Emil Bjerrum Bohr, Dave Dunbar and Harald Ita.
A bootstrap approach to loop amplitudes.
Presented at
Loops and and Legs in Quantum Field Theory 2006
Precision Calculations for the LHC. Presented at
LHC Olympics 2006
On-Shell Methods in Perturbative QCD. Presented at
ICHEP 2006
One loop amplitudes for e+ e- to four partons
Bootstrapping multi-parton loop amplitudes in QCD
Recursive calculation of one-loop QCD integral coefficients
Bootstrapping One-Loop QCD Amplitudes with General Helicities
All One-loop Maximally Helicity Violating Gluonic Amplitudes in QCD
Conventional wisdom holds that no four-dimensional point-like quantum gravity field theory can be ultraviolet finite. This understanding is based mainly on power counting. But is this really true? Based on our work we now have good reason to believe it is not. Were a finite four-dimensional point-like theory of gravity to be found, either a new symmetry or non-trivial dynamical mechanism would underpin it. The discovery of either would have a fundamental impact on our understanding of gravity.
In 1998, together with Lance Dixon, Dave Dunbar, Maxim Perelstein and Joel Rozowsky, we developed a new method for studying the ultraviolet properties of quantum gravity theories. In 2004 Dave Dunbar, Emil Bjerrum-Bohr and I formulated what is referred to as the "no-triangle hypothesis''. This hypothesis states that that in the most supersymmetric theory of gravity, N=8 supergravity (discovered by Cremmer, Julia and Scherk in 1978), special cancellation happen in all one-loop amplitudes of the theory. Such cancellations were first observed a number of years by Lance Dixon, Maxim Perelstein, Joel Rozowsky and myself, in a special class of amplitudes known as maximal helicity violating amplitudes. With use of the unitarity method it was clear that this induces cancellations at higher loops which could very well render the theory to be ultraviolet finite, as described in a number of my early talks on the subject. These cancellations were outlined in a paper with Lance Dixon and Radu Roiban, and explicitly shown to hold at three loops in a recent paper with Lance Dixon, David Kosower, Radu Roiban and two UCLA graduate students, John Joseph Carasco and Henrik Johansson. This paper provides direct evidence of the existence of novel cancellations, strongly suggesting perturbative ultraviolet finiteness of the N=8 theory.
We hosted a workshop on the question of ultraviolet finiteness in N=8 supergravity at UCLA in December 2006: Is N=8 supergravity finite?
Supergravity from QCD Amplitudes. Presented at
KITP January 2004
The S-Matrix Reloaded: Twistors, Unitarity, Gauge Theories and Gravity,
(see pages 31-35). Presented at KITP
September 2005
The S-Matrix Reloaded: Twistors, Unitarity, Gauge Theories and Gravity
(newer version) see pages 40-45. Presented at
Niels Bohr Summer Insitute 2006
Maximally supersymmetric N = 4 Yang-Mills theory in four dimensions has a number of remarkable properties. There are good reasons to believe that, in the 't~Hooft (planar) limit of a large number of colors, higher-loop orders are surprisingly simple. In particular, Maldacena's AdS/CFT correspondence suggests a simplicity in the perturbative expansion of planar N = 4 super-Yang-Mills theory as the number of loops increases. The Maldacena conjecture states that the planar limit of N = 4 super-Yang-Mills theory at strong coupling is dual to weakly-coupled gravity in five-dimensional anti-de Sitter space. Based on this conjecture, one might expect observables in the strongly-coupled limit of to have a relatively simple form, due to its interpretation in terms of weakly-coupled gravity.
Inspired by our two-loop calculations as well as by Maldacena's conjecture, Babis Anasasiou, Lance Dixon, David Kosower and I conjectured a simple iterative relation for the planar scattering amplitudes of N = 4 super-Yang-Mills theory, suggesting that it might be possible to write down all scattering amplitudes in the planar limit. This conjecture was fleshed out together with Lance Dixon and Volodya Smirnov, providing a precise form for the iteration for maximally helicity violating amplitudes. At four loops, using an explicit construction of the planar amplitudes, we computed the four-loop cusp anomalous dimension. By applying Pade and other approximation schemes, we obtained an estimate for the leading coefficient of the strong coupling expansion within 2.6 percent of the string theory prediction. This provides rather non-trivial evidence in favor of Maldacena's AdS/CFT correspondence.
The S-Matrix Reloaded: Twistors, Unitarity, Gauge Theories and Gravity,
Presented at
KITP September 2005,
The S-Matrix Reloaded: Twistors, Unitarity, Gauge Theories and Gravity
(see pages 20-38).
Presented at
Workshop on Integrability in Gauge and String Theory July 2006.
Two loop four gluon amplitudes in N = 4 superYang-Mills
Planar amplitudes in maximally supersymmetric Yang-Mills theory
Iteration of planar amplitudes in maximally supersymmetric Yang-Mills
theory at three loops and beyond
The four-loop planar amplitude and cusp anomalous dimension
in maximally supersymmetric Yang-Mills theory