Surprises at Infinity

8 April 2026

Photo: UHH/Monnee, this image was created with the assistance of ChatGPT

Artistic impression of quantum moduli space, a parameter space of a quantum gravity theory.

Physicists often explore the edges of what is possible—pushing theories to their limits to understand how they work. But what if some of those limits don't actually exist?

The basic idea

In theoretical physics, a common strategy for tackling complicated problems is to study extreme situations. For example, if particles interact only very weakly, calculations become much easier and can be done step by step.

In a theory of quantum gravity, however, things become more subtle. Quantities we usually think of as fixed numbers—like how strongly particles interact—may actually vary. Their values can depend on other fields in the theory. This is similar to the Higgs field in the Standard Model, whose value determines the masses of elementary particles.

String theory, one of the main candidates for a theory of quantum gravity, makes this idea more concrete. It suggests that our universe has more than four dimensions. The extra dimensions are thought to be curled up into tiny shapes that we cannot directly observe. The exact way they are curled up can influence the physics we see.

In these theories, different possible versions of the universe can be described by changing certain parameters (called moduli), such as the shape of the extra dimensions. You can think of all these possibilities as forming a kind of “space of solutions.” Some especially simple situations lie at the extreme edges of this space, at infinity in the space of solutions, where interactions become very weak. Physicists often study these limits because they make calculations easier.

However, in two papers posted on the arXiv in March 2026, Cluster of Excellence Quantum Universe researchers Lukas Kaufmann, Jeroen Monnee, Timo Weigand, and Max Wiesner show that this expectation can be misleading. They find that situations which seem perfectly consistent when quantum effects are ignored can break down once those effects are taken into account. In some cases, the limit is not just difficult to reach — it may not exist at all in the full quantum theory.

To arrive at this result, the researchers combine sophisticated ideas from geometry and quantum field theory. In simple terms, they study how the shape of extra dimensions affects physical predictions and how quantum effects can modify this picture in subtle but important ways.

Their work shows that theories of quantum gravity can behave very differently from more familiar theories. In particular, quantum effects can drastically change situations that at first seem simple and well understood.

This is especially important for attempts to build realistic models of our universe. A model that appears perfectly consistent at first may turn out to be inconsistent once quantum effects are included. This idea is closely related to a modern research direction that aims to identify which theories of quantum gravity are truly consistent, the so-called Swampland Program.

Why this is surprising

What makes these results striking is that these extreme limits are usually seen as reliable starting points. Physicists often use them to simplify problems and to separate complicated systems into smaller, more manageable pieces.

The new work shows that this approach can fail. Effects that are usually assumed to be negligible can instead become important precisely in the regime where one expects the most control.

It also suggests that different parts of the theory are more strongly connected than previously thought. Changing one quantity can strongly affect others. This makes the theory more constrained and shows that commonly used simplifications may miss important feedback effects.

Why this matters for model building

Many approaches to constructing realistic models in string theory rely on working in extreme limits, where calculations are easier and corrections are expected to be small. This is particularly important when trying to fix the values of the many parameters that appear in these theories.

The new results show that this strategy can break down. A situation that looks promising at first may turn out to be unstable—or may not exist at all once quantum effects are properly included.

This does not mean that building realistic models is impossible. But it does mean that greater care is needed and that the range of consistent models may be more limited than previously thought.

At the same time, this work may shed new light on an important open question: whether string theory can describe a universe like ours, which appears to have a small positive energy density even in empty space.