Strings in physics don't just vibrate: they live in a space that itself can change its properties. Sometimes, additional fields, akin to invisible lines of force, are superimposed on this space. In a new study, scientists figured out how such fields affect geometry in heterotic string theory — a variant of string theory where vibrations can be 'left-handed' and 'right-handed'.
They introduced the notion of 'dressed' geometry: imagine spacetime itself putting on an extra layer — a field that slightly alters distances. This is like a thin film on a mirror that distorts the reflection. Mathematically, the metric, the quantity that defines how distances are measured, gets shifted. It turns out that this shift allows building new structures reminiscent of complex numbers but more exotic.
The main result is an analogue of Buscher's rule for heterotic strings. The usual Buscher rule is a transformation that relates large and small geometries: for example, a universe the size of a pea and a universe the size of a galaxy. The authors showed how a similar transformation works when non-Abelian gauge fields are included — fields that don't just add up but interact with each other, like colors in a complex painting.
In the end, the physicists obtained an extended Born geometry governed by the algebra of hypercomplex numbers. It's as if familiar numbers suddenly gained extra dimensions and began to follow new laws. Such a mathematical framework could be useful for describing symmetries in more realistic string theory models, where fields and geometry are even more tightly intertwined.
T-duality in string theory means that a universe curled into a circle of radius R is physically indistinguishable from a universe of radius 1/R. If we lived in such a universe, we couldn't tell whether it's huge or microscopic.
In Iain Banks's novel 'Excession', a civilization is described that can alter the geometry of space, creating pocket universes with different physical laws — almost like the 'dressed' geometry from the paper.