(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Part C) Please:

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):

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?

Many thanks in advance.

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# Homework Help: QFT T-duality, Massless vector states

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