However, it is very hard to confirm or disprove the
conjecture in practice.
Nevertheless, a lot of progress has been achieved in recent
years for the most symmetric form of the AdS/CFT correspondence,
which involves a symmetry group called PSU(2,2|4). In this case,
strong indications of integrability have been found. The power
of an integrable system is that one can solve its spectrum
exactly using the Bethe ansatz.
In the present paper we propose Bethe equations for this
maximally symmetric AdS/CFT system. What is especially exciting
is that it offers a way to obtain exact results in a highly non-trival
four-dimensional gauge theory. These can in turn be used for
very precise confirmations of the AdS/CFT correspondence.
How
did you become involved in this research, and were there obstacles
along the way?
We became involved in the field of AdS/CFT integrability
shortly after the appearance of the seminal paper by Joseph A.
Minahan and Konstantin Zarembo of Uppsala University's Dept. of
Theoretical Physics, who discovered an integrable system in a
sector of planar maximally supersymmetric gauge theory at
leading order.
In early 2003 we observed a curious two-fold degeneracy in
the spectrum of the planar maximally supersymmetric gauge
theory. Together with Charlotte Kristjansen of Nordita, in
Copenhagen, we realized that this vastly generalizes the
Minahan and Zarembo result and that the complete planar
gauge theory model might be exactly solvable.
This particular paper started out as a simple result of how a
particular Taylor series could be written in a simple closed
form.
This was merely one piece of a bigger puzzle and many others
were already laid out. But it gave us some insight of what the
adjacent pieces would have to look like, and we quickly found
them. These again revealed a greater picture and more pieces
followed. At some point the patches did not quite seem to fit
together. After some point we figured out that we could soften
one expected feature which allowed us to move everything else
into place and to get a complete overall picture. Although we
had no formal proof of the correctness of our conjecture,
everything fit so beautifully that it simply had to be true. In
subsequent publications we could then establish rigorous proofs
of our conjectured equations.
Does
it describe a new discovery, methodology, or synthesis of knowledge?
This is not quite clear yet. On the one hand the paper does
not represent a new discovery or methodology as such. On the
other, the fundamental system underlying our equations is not
quite known yet and might contain entirely novel features.
Finding it might open the door for many new applications in
distinct fields such as condensed matter theory.
The overall structure of our proposed equations was more or
less obvious and some pieces of them were already known. What
was not known when we started this project was if a suitable
system of equations exists, and if it can be written in a
reasonably nice exact form. And, clearly, the precise form of
all the terms in the equations is required to perform any sort
of calculation with them.
In our paper we argued that the answer to the two equations
is "yes." by proposing a complete self-consistent system of
equations up to one unknown function. In recent collaborations
with Esperanza Lopez, Rafael Hernandez and Burkhard Eden, we
were even able to make a consistent proposal for this remaining
undetermined function.
Are
there any social or political implications for your research?
No direct ones that we are aware of. But maybe one could
stress that the creation of this topic is a beautiful example
for international cooperation. We believe it would not have
evolved so rapidly without the current means of rapid
communication through the Internet, in particular, email and the
arXiv. The latter largely marginalized the traditional way of
transmitting information through mailed preprints and printed
journals.
It is also nice that many crucial contributions in this field
were achieved in Europe, and we believe the main reason for this
is that the investments in fostering European science through a
mix of European "networks," financed by the EU and national
programs such as provided by the German Max-Planck-Society, is
really beginning to pay off.
Niklas Beisert & Matthias Staudacher
answer a few questions about this month's
new hot paper in the field of Physics.
The authors have also
sent along images of their work.
