The Young Investigator's group "Nonlinear Sigma Models in String Theory lead by J. Teschner (Marie Curie Excellence Grant MEXT-CT-2006-042695) studies sigma models relevant for string theory with the help of techniques from the theory of integrable models).

Motivation:

The real differences between a string and a point particle will show up if the string moves on a curved space-time. The quantum effects will depend strongly on the geometry in which the string moves, and will lead to important new effects compared to the motion of point-particles. Understanding such effects is foundational for applications of string theory to cosmology or black hole physics. These effect may force us to modify the basic geometrical concepts by which we describe nature. What is needed are explicitly solvable examples which illustrate the new effects.

The slides of a lecture for a general audience which explains some of this motivation can be found here:

Lecture (1.5 MB)

String-Theory.pdf

Slides from the lecture held on February 28th 2011 at DESY main auditorium.

Apart from this, thanks to the famous AdS-CFT-correspondence it is possible to use results about string theory on a special class of curved space-times for the study of gauge theories, which are the theories for the strong interactions binding together the fundmantal constituents of matter. The space-times in question are called the Anti-De Sitter spaces. There is growing evidence for the conjectures of Maldacena on exact equivalences between string theories on certain Ant--De Sitter spaces with corresponding gauge theories. In a particular example both are expected to be exactly solvable, which would lead to highly nontrivial checks of this correspondence and deep physical insights. Even though indirect evidence has been gathered for the solvability in the example of stringtheory on a five-dimensional Anti-De Sitter space, see e.g. the review by N. Beisert and friends, it remains to be shown directly that this conjecture is indeed true.

The most promising approach to this problem is to start by proving the solvability of the string theory in question, which boils down to proving the complete solvability of an auxilliary quantum field theory in two (one space, one time) dimensions which is called Nonlinear Sigma Model. This goal is what motivates our project.↵

Aims of our project:

The aim of our project is to develop the tools for the construction of solvable string theories on curved spaces, and the mathematical techniques for the calculation of physically interesting quantities. In order to prove that a Nonlinear Sigma Model has the property to be completely solvable, which is often referred to as the integrability of the model, one has to construct sufficiently many quantities which remain constant in the quantum time-evolution of the model. While the origin of the difficulties encountered in this procedure is standard (the usual divergencies of quantum field theory), it is still quite challenging to address these difficulties in a way that makes the integrability of the two-dimensional auxilliary quantum field theory in question manifest. The most promising approach known at present is to approximate the underlying two-dimensional space by a lattice with field variables assigned to the different sites of the lattice respectively. The quantum field theory of interest gets thereby approximated by a quantum mechanical system, from which the theory of interest can be recovered in the limit when the distance between adjacent lattice sites tends to zero. The main problem to be addressed can be formulated as follows: Assume we have a description of the time-evolution in our auxilliary two-dimensional field theory on the classical level, can we construct a corresponding quantum theory with integrable time evolution on a two-dimensional space-time lattice, which defines the quantum field theory of interest in the limit where the distance between adjacent lattice sites vanishes?

Former members of the young investigator's group

Juliane Grossehelweg (finished Ph.D. 05/2010, now d-fine Consulting)
Karol Kozlowski (still DESY-Theory)
Giuliano Niccoli (now Pstdoc at YITP, Stony Brook University, New York)
D. Ridout (now five-year Australian Research Fellow at the Australian National University,Canberra)
Joerg Teschner (still DESY Theory)

Long-term visitors:

A. Bytsko (Steklov Institute for Mathematics, St. Petersburg)
F. Ravanini (Dep. of Physics, Univ. Bologna and INFN, Sezione di Bologna)
F. Smirnov (CNRS, LPTHE Jussieu, Univ. Paris 6/7)

Publications:

Selected Results