Question

State space of strings: Spin-1 particles in the conformal gauge?

Answer 1

By "spin", do you mean the kind of SO(D−2)SO(D−2)representation (vector, traceless symmetric tensor), or do you mean the component of the spin, for instance S12S12, for some specific state

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Answer 2

HEY MATE ⭐⭐⭐
HERE'S THE ANSWER ✌
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there are usually two common gauge to solve the classical problem and quantize the strings:

lightcone gauge
conformal gauge.
After quantization, you study the state space, and here I have a problem with probably the representations of the SO(24)SO(24) (I focus on bosonic strings). I explain my problem explicitly below:

1-in lightcone gauge: for the second excited state, N=2N=2 : the mass is M2=1/α′M2=1/α′ and the bases for this subspace are : aμ2|0⟩a2μ|0⟩ and aμ1aν1|0⟩a1μa1ν|0⟩

2- in the conformal gauge: for the second excited state, N=2N=2 : M2=1/α′M2=1/α′ and the bases for this subspace are: aμ1aν1|0⟩a1μa1ν|0⟩ and, not aμ2|0⟩a2μ|0⟩.

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