A clay ball is kneaded in your hands, changing shape but not tearing — some parts stretch, others compress. That's roughly how physicists work with spacetime, except their fingers are equations and their clay is a six-dimensional world.
Scientists took a space known as anti-de Sitter (where distances behave differently than in an ordinary room: parallel lines can diverge or converge) and applied a transformation — T-duality. It changes the geometry of the world: where it was smooth, a fold appears, spacetime curvature, like a point where the clay thins to nothing. In physics, such a point is called a singularity.
The authors checked: at small distances, where the clay is compressed, the new world contains a rupture. But the equations of quantum theory, the so-called beta functions, remain in equilibrium. And at large distances, when we look at the ball from afar, both worlds, the original and the dual, look the same. Like two prints of the same palm on different pieces of clay.
Finally, the researchers studied how D-branes, objects on which string ends can attach, behave in these worlds. It turned out that duality links branes into a chain: like reflections in two mirrors placed facing each other, multiplying to infinity, but each link obeys a strict symmetry.
as written by the authors arXiv:2607.10448
We proceed to construct a non-Abelian dual pair for the $$AdS_2 \times H^2 \times H^2$$ background by applying the non-Abelian T-duality (here as Poisson-Lie T-duality on a semi-Abelian double). By using a certain parameterization of the $$6$$-dimensional Lie group $${A}_2 \otimes {A}_2 \otimes A_2$$ we construct the original $$\sigma$$-model including the $$AdS_2 \times H^2 \times H^2$$ metric in the absence of $$B$$-field. It is shown that the dual background constructed by means of the Poisson-Lie T-duality is supported by a $$B$$-field and a metric whose contains a physical singularity. By studying the behavior of the dual spacetime at small $$(r , y, u)$$ coordinates, we show that the dual metric with a zero field strength and a non-trivial dilaton field make up a solution for the vanishing of the one-loop beta-function equations. Furthermore, at large $$(r , y, u)$$, it is shown that the $$AdS_2 \times H^2 \times H^2$$ solution is preserved under the non-Abelian T-duality. Finally, using the duality map obtained from the canonical transformation description of the Poisson-Lie T-duality for the gluing matrix which locally defines the properties of the D-brane, we find seven different cases of the gluing matrices for the $$AdS_2 \times H^2 \times H^2$$ $$\sigma$$-model and its dual pair. In this way, it is found a symmetric duality action on the branes linking together in a duality chain.
T-duality is like the trick of turning a sock inside out: you flip it, and it becomes a different thing, but essentially it's still the same sock. In physics, similarly: a space with a tiny radius can turn out to be equivalent to a space with a huge radius.
In Carl Sagan's novel "Contact," the heroine travels through a wormhole woven from unknown geometry. Dual transformations are one of the tools physicists hope will someday describe such tunnels without paradoxes.