### T Duality

Now that String Theory has officially won the String Wars* (by changing its thinking radically enough to finally look like it is on the right track) it is worth making a simple point about T duality.

In modern physics, almost everything is measured in terms of energy. Distance is an inverse energy, temperature is an energy, and so on. For a basic black hole, the mass of a black hole goes like the inverse of a Hawking temperature. In other words, mass is somehow like an inverse energy, which is the distance scale of the black hole radius.

But mass is just an energy. So even without considering any kind of string theory at all, we should expect T duality to play an important role in gravity.

In a non local theory, however, it does no good to talk about a priori distance scales. At the fundamental level, black hole properties arise from considerations of, say, their information content. It is expected that a classical spacetime, with its notion of horizon scale, should only arise as a thermodynamic collection of such quantum states. So where is the T duality? It can only be in the mass quantum numbers. Distances are derived from the masses, but they are not inherently properties of the quantum states. This suggests that a rigorous T duality for Yang-Mills theory is closely related to the issue of a mass gap, because the limit of the Planck scale is replaced by a minimal, or dually maximal, mass.

*AF will still occasionally refer to string theorists as idiots, and the correct theory as M theory.

In modern physics, almost everything is measured in terms of energy. Distance is an inverse energy, temperature is an energy, and so on. For a basic black hole, the mass of a black hole goes like the inverse of a Hawking temperature. In other words, mass is somehow like an inverse energy, which is the distance scale of the black hole radius.

But mass is just an energy. So even without considering any kind of string theory at all, we should expect T duality to play an important role in gravity.

In a non local theory, however, it does no good to talk about a priori distance scales. At the fundamental level, black hole properties arise from considerations of, say, their information content. It is expected that a classical spacetime, with its notion of horizon scale, should only arise as a thermodynamic collection of such quantum states. So where is the T duality? It can only be in the mass quantum numbers. Distances are derived from the masses, but they are not inherently properties of the quantum states. This suggests that a rigorous T duality for Yang-Mills theory is closely related to the issue of a mass gap, because the limit of the Planck scale is replaced by a minimal, or dually maximal, mass.

*AF will still occasionally refer to string theorists as idiots, and the correct theory as M theory.

## 2 Comments:

"T duality" has a very specific meaning, and as far as I can tell your post has nothing to do with it. I think it's counter-productive to abuse terminology in this way.

But what if the standard terminology has no relation whatsoever to the real world? Then surely it is counterproductive to insist on the standard definition (and I don't actually agree that there is a completely specific meaning) long after its expiry date.

As they say ... adapt or die.

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