Why are open strings vectors or scalars, or massive?

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SUMMARY

In string theory, the boundary conditions (BCs) significantly influence the nature of excitations, resulting in massless vectors and scalars. Specifically, with Neumann (NN) BCs along dimensions ##X^i## (for ##i = 1, \ldots, n-1##) and Dirichlet (DD) BCs along dimensions ##X^a## (for ##a = n, \ldots, 25##), the excitation states yield ##n## massless vectors and ##24-n## massless scalars. The mass squared, ##M^2=0##, indicates no mass for the first excited level, while the tensorial nature of these excitations is determined by the indices of the creation operator, specifically ##\alpha^{i,a}_{-1}|0,p\rangle##.

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  • Understanding of string theory concepts, particularly boundary conditions.
  • Familiarity with massless particle states in quantum field theory.
  • Knowledge of creation operators and their indices in string theory.
  • Basic grasp of the relationship between branes and excitation states.
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  • Study the implications of Neumann and Dirichlet boundary conditions in string theory.
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The discussion is beneficial for theoretical physicists, string theorists, and advanced students in physics who are exploring the intricacies of string theory and the implications of boundary conditions on particle excitations.

Maurice7510
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In string theory, if we have NN BCs along ##X^i, i = 1, \ldots, n-1##
and DD BCs along ##X^a, a = n, \ldots, 25## then you get, from ##\alpha^{i,a}_{-1}|0,p\rangle ##, ##n## massless vectors and ##24-n## massless scalars. I understand that for the first excited level, ##M^2=0## and so we have no mass, but what suggests that these are scalars or vectors? In the case where we have two branes separated by a distance ##\delta##, with find ##M^2\propto\delta^2## which, in addition to the vector/scalar nature of the excitations, I don't understand.
 
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Their tensorial nature is determined by the index of the creation operator, no?
 
I'm not sure how that would be the case though; the indices on the creation operator are ##i## (or ##a##) and ##-1##. The lower index is the state number (i.e. ##\alpha_{-1}## creates a one particle state) and the upper indicates indicate whether the BCs are NN or DD.
 

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