# Why are open strings vectors or scalars, or massive?

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• Maurice7510
In summary, in string theory, if we have NN boundary conditions along ##X^i## and DD boundary conditions along ##X^a##, we get ##n## massless vectors and ##24-n## massless scalars from the state ##\alpha^{i,a}_{-1}|0,p\rangle##. The mass for the first excited level is ##M^2=0##, suggesting no mass, but it remains unclear what determines the vector/scalar nature of the excitations. In the case of two separated branes with a distance ##\delta##, the mass is proportional to ##\delta^2## and the nature of the excitations remains unclear. The tensorial nature is determined by the index of
Maurice7510
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.

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.

## 1. Why are open strings considered vectors?

Open strings are considered vectors because they have two independent directions of oscillation: left-right and up-down. These directions can be visualized as two axes, similar to the x and y axes in a graph. Therefore, open strings exhibit properties of vectors, such as being able to be added and multiplied by scalars.

## 2. Why are open strings not considered scalars?

Unlike scalars, open strings do not have a single value or magnitude. Instead, they have a direction and can be stretched or contracted. This is why they are considered vectors rather than scalars.

## 3. Are open strings massive or massless?

Open strings can have both massless and massive states, depending on the energy of their oscillations. In a massless state, the open string is stretched to its maximum length and has no oscillations. In a massive state, the open string has oscillations and therefore has energy and mass.

## 4. Why do open strings have two ends?

Open strings have two ends because they are not closed loops like closed strings. The two ends allow for the string to vibrate and produce different frequencies, which correspond to different particles in string theory.

## 5. How do open strings differ from closed strings?

Open strings have two ends and can vibrate in two independent directions, while closed strings have no ends and can only vibrate in one direction. Additionally, open strings have both massless and massive states, while closed strings only have massive states. These differences have significant implications in string theory and the behavior of particles.

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