# Research

# String Theory

## Research

String theory is an interdisciplinary field of fundamental research, with very fruitful interfaces to high energy physics, general relativity, cosmology, statistical physics and mathematics. It currently addresses two distinct and fundamental problems of modern theoretical physics: The unification of all interactions, including gravity, and the physics of strongly interacting quantum field theories.

##### Supersymmetric gauge theories

Gauge theory provides the theoretical framework with which we describe the world we live in. It is very successful as long as particles interact weakly, however, in the strong coupling regime, major theoretical challenges remain unsolved. Our understanding of non-perturbative phenomena, such as confinement, is very limited (see here for a description of the problem), majorly due to the lack of a quantitative understanding of the theory in regimes with strong interactions among gluons and quarks. Supersymmetric gauge theories provide a theoretical laboratory within which we can explore the strong coupling regime of gauge theories and quantitatively understand non-perturbative phenomena. In many cases they even provide examples of theories or observables with can be solved exactly (see here for recent review). What is more, supersymmetric gauge theories are intimately related to string theory. Gauge theories can emerge as low-energy limits of string theories, and string theories can describe gauge theories at strong coupling providing us qualitative tools. This profound interplay is investigated and exploited in our research in order to learn more about gauge theory and string theory in regimes which are very hard to access by more conventional methods.

##### Conformal field theories

Scale invariant theories are ubiquitous in the study of quantum field theories, arising naturally in their low energy behaviour. Most physically relevant scale invariant theories are invariant under a larger symmetry, exhibiting conformal symmetry. The study of Conformal Field Theories (CFTs) is also connected with that of string theory in anti-de-Sitter space through a holographic duality (see for example here). The DESY string theory group is actively studying CFTs from different fronts. One such approach is through the so-called conformal bootstrap approach to CFTs, both in two dimensions and beyond, with the latter having seen much progress in recent years (see here for a review of the recent progress on the subject). In short, these are revivals of the old idea that symmetry constraints, allied with general consistency requirements, could be powerful enough to solve theories. The special case of two-dimensional CFTs allows for rich connections to mathematics, and is also an active subject of research, in close collaboration with the mathematics department at the Hamburg University (see here for a recent guide to two-dimensional CFTs).

##### Integrability

Exact results in physics are precious, they give us a deeper understanding of the dynamics of a theory, together with strong analytical control. Integrability refers to the presence of additional, often hidden symmetries. Integrable theories turn out to be exactly solvable due to the enhanced symmetry. Such exactly solvable structures appear both in quantum field theory and string theory. Although integrable structures have played an important role in low-dimensional systems, since the early 2000s impressive progress has been made in the uncovering of integrability in higher dimensional field theories. For this reason, the paradigmatic example of 4d maximally supersymmetric Yang-Mills theory has been dubbed “the harmonic oscillator of the 21st century” (see here for a review). The DESY theory group is active in integrability research, with a particular emphasis on bridging the gap to other areas of modern physics, like the theory of scattering amplitudes and the conformal bootstrap program.

##### Scattering amplitudes

Scattering amplitudes form a bridge connecting theoretical particle physics with the real world of collider experiments, yielding the probability of specific outcomes when quantum particles interact. Although their computation by means of Feynman diagrams quickly becomes prohibitive, and is only valid when the particles are interacting weakly, members of the DESY String theory group are making significant progress addressing these shortcomings, also in close contact with their Phenomenology group colleagues: By exploiting the mathematical structure and analytic behavior of amplitudes, as well as the integrability and dual string description of simple gauge-theoretic models, they develop new efficient methods for their computation, all the way from weak to strong interaction strength (see here for a review).