A quantum calculation sometimes resembles an interpreter who gets distracted by every rustle in the hall, and a one-hour meeting turns into two. In physics, such a "rustle" is called the sign problem: it arises when probabilities in formulas become negative or complex, and ordinary computer simulations start to fail. This is especially acute in theories with fermions — the particles that make up matter.

A group of physicists proposed an elegant workaround. They built a "bridge" between worlds: at high temperatures, a complex spacetime theory with fermions simplifies to a bosonic theory in fewer dimensions. The phase of a special quantity — the Pfaffian (a kind of "square root" of the determinant)—which creates the sign problem, turns into an operator inside the simpler bosonic integral. They applied this method to the D0-brane model — tiny objects that arise in string theory.

The result surprised them: in the continuous theory, the sign problem does not disappear, but its influence is postponed until the tenth order in the high-temperature expansion. The reason lies in symmetry: the Pfaffian phase behaves like a pseudoscalar in nine-dimensional space, and such quantities do not contribute at lower orders. Moreover, the numerical coefficient in front of the relevant diagrams turned out to be very small. Therefore, for temperatures above a certain threshold, the error from neglecting the sign remains modest — on the order of a few percent.

Ten loops in the high-temperature expansion is like accounting not just for the first steps of a particle, but for its wandering with ten turns. Each turn adds computations, but also reveals new effects.

However, when the coupling is strengthened (in the so-called 't Hooft regime), the sign problem may become more serious. The authors have also begun to extend their approach to more realistic supersymmetric Yang-Mills theories in higher dimensions. So the interpreter gets noise-canceling headphones, and the meeting proceeds almost without delays.