# What does the "T" stand for in T-duality?

First of all, I am not a physicist. I'm a graduate math student and recently I came across the concept of T-duality. Actually I'm studying generalized complex geometry, which according to this paper (Generalized complex geometry and T-duality) can be used to get some nice interpretations of T-duality.

After reading some of it, I thought the "T" stand for torus, because the the fiber are torus. But then I found another paper (Spherical T-duality) defining T-duality for $SU(2)$-bundles. At first I asked myself "Why keep calling it T-duality, if the fiber are not torus anymore?" Probably it means something else...

So, what does the "T" stand for in T-duality?

• It is probably just historical -- when it was first discovered “T" was for torus (strings compactified on torus/cylinder). Commented Mar 29, 2015 at 18:22
• Related meta post: meta.physics.stackexchange.com/q/1083/2451 Commented Mar 29, 2015 at 21:07

The name T-duality stands for Target-space duality, Topological duality, or Toroidal duality, depending on whom you ask. See e.g. this preprint or this book.

• Reminds me of Witten's answer when he was asked what the 'M' in M-theory stands for :) Commented Dec 5, 2020 at 13:48

T duality and S duality come from the $T$ transformation and $S$ transformation which generate the modular group $PSL(2,\mathbb{Z})$.

It comes from S matrix theory, long before quarks were imagined, S,T and U characterize the type of exchange in the Feynman diagrams entering the S matrix calculation, and they are called Mandelstam variables.

s channel-------------------------- t channel------------------------u channel

duality meant that the sums could be done either in S channel or T channel and the result should be the same.

There is a resurrection of the scattering matrix for strings and I guess the definition has morphed to what you find in the link you gave.

It is also used in nuclear physics, where dualities are useful.

The above is history of theory in particle physics, and it was T because it came after the S of Scattering ( like y after x).