T-duality relates type IIA superstring theory to type IIB superstring theory. This type of duality is called T-duality. So exchanging momentum and winding modes of the string exchanges a large distance scale with a small distance scale. Winding around the circle requires energy, because the string must be stretched against its tension, so it contributes an amount of energy of the form w R / L s t 2 and switching n and w will yield the same equations. The number of times the string winds around the circle is called the winding number, and that is also quantized (as it must be an integer). A string, in addition to traveling around the circle, may also wrap around it. In fact, the particle momentum around the circle - and the contribution to its energy - is of the form n/R (in standard units, for an integer n), so that at large R there will be many more states compared to small R (for a given maximum energy). A particle traveling around this circle will have a quantized momentum around the circle, because its momentum is linked to its wavelength (see Wave-particle duality), and 2πR must be a multiple of that. Take one of those nine space dimensions and make it a circle of radius R, so that traveling in that direction for a distance L = 2πR takes you around the circle and brings you back to where you started. Suppose we are in ten spacetime dimensions, which means we have nine space dimensions and one time. But strings can obscure the difference between large and small, strong and weak, and this is how these five very different theories end up being related. These quantities have always marked very distinct limits of behavior of a physical system, in both classical field theory and quantum particle physics. String dualities often link quantities that appear to be separate: Large and small distance scales, strong and weak coupling strengths. A simple example of a duality is the equivalence of particle physics upon replacing matter with antimatter describing our universe in terms of anti-particles would yield identical predictions for any possible experiment. Put differently, the two theories are two mathematically different descriptions of the same phenomena. The two theories are then said to be dual to one another under that transformation. If two theories are related by a duality transformation, each observable of the first theory can be mapped in some way to the second theory to yield equivalent predictions. These theories are related by transformations called dualities. It is now known that the five superstring theories are not fundamental, but are instead different limits of a more fundamental theory, dubbed M-theory. The thinking was that out of these five candidate theories, only one was the actual theory of everything, and that theory was the theory whose low energy limit, with ten dimensions spacetime compactified down to four, matched the physics observed in our world today. Note that in the type IIA and type IIB string theories closed strings are allowed to move everywhere throughout the ten-dimensional space-time (called the bulk), while open strings have their ends attached to D-branes, which are membranes of lower dimensionality (their dimension is odd - 1,3,5,7 or 9 - in type IIA and even - 0,2,4,6 or 8 - in type IIB, including the time direction).īefore the 1990s, string theorists believed there were five distinct superstring theories: type I, types IIA and IIB, and the two heterotic string theories ( SO(32) and E 8× E 8). Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is E 8× E 8 Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is SO(32) Supersymmetry between forces and matter, with closed strings and open strings bound to D-branes, no tachyon, massless fermions only spin one way (chiral) Supersymmetry between forces and matter, with closed strings and open strings bound to D-branes, no tachyon, massless fermions spin both ways (nonchiral) Supersymmetry between forces and matter, with both closed strings and open strings, no tachyon, group symmetry is SO(32) Only bosons, no fermions means only forces, no matter, with both open and closed strings major flaw: a particle with imaginary mass, called the tachyon, representing an instability in the theory. Before the so-called "duality revolution" there were believed to be five distinct versions of string theory, plus the (unstable) bosonic and gluonic theories.
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