# QFT T-duality, Massless vector states

#### binbagsss

1. The problem statement, all variables and given/known data

Part C) Please on first attachment

2. Relevant equations

above,below

3. The attempt at a solution

so I think I understand the background of these expressions well enough, very briefly, changing the manifold from $R^n$ to a cylindrical one- $R^{(n-1)}^{+1}$ we need to cater for winding modes, the momentum and winding momentum for the circular dimension can not take arbitrary values and are quantified, $n,m \in Z$

And importantly, the level-matching constraint is no longer required to hold and instead replaced by the second equation in c) .

For the combinations I get:

a) $n=m=0$ $N=\bar{N}=1$
b) $n=m=1=N$ $\bar{N}=0$
c) $n=2$ $m=0=N=\bar{N}$
d) $m=2$ $n=N=\bar{N}=0$

I am completely stuck on which of these combinations transforms as a vector. The only notes relevant to it I seem to have is the following attached, (bit underlined in pink):

2nd attachment

Is this referring to the ladder operator carrying a transverse index? or the state |p> ?

So out of the combinations above I have:

a) would require both a $\alpha^j$ and a $\bar{\alpha^j}$
b) would require just a $\alpha^j$
c) & d) would require no ladder operators.

Is the above relevant/needed at all or not, for what transforms as a vector or what doesn't, what defintion am I needing to go by here?

#### Attachments

• 21.6 KB Views: 1
• 33.6 KB Views: 1

#### lovebunny

This really does not work since a quantum implies a particle field structure but Maxwell's electromagnetic field is expanding which cannot maintain a particle structure. Why is this basic concept so difficult to comprehend?

#### topsquark

Forum Staff
This really does not work since a quantum implies a particle field structure but Maxwell's electromagnetic field is expanding which cannot maintain a particle structure. Why is this basic concept so difficult to comprehend?
Because String Theory is a "high energy" version of QFT. The vibrations on the string are the quanta.

And all fields "expand". Please continue this idea in the Lounge if you want to talk about it.

-Dan