# Problem 14.4a1

Closed string degeneracies | A First Course in String Theory

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(a) State the values of $\alpha' M^2$ and give the degeneracies for the first five mass levels of the closed bosonic string theory.

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What is the meaning of “closed bosonic string theory”?

Bosonic? Meaning commutating creation operators?

Closed?

String? Or superstring?

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p.308 “We describe the position of classical bosonic strings using the string coordinates $X^\mu(\tau, \sigma)$. The $X^\mu(\tau, \sigma)$ are classical commuting variables: …

In quantum theory the $X^\mu$‘s become operators that do not generally commute.”

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“To get fermions in string theory we introduce new dynamical world-sheet variables $\psi_1^\mu(\tau, \sigma)$ and $\psi_2^\mu(\tau, \sigma)$. The classical variables $\psi_\alpha^\mu$ ( $\alpha = 1, 2$) are not ordinary commuting variables, but rather anticommuting variables.”

p.324 “In closed superstring theories spacetime bosons arise from the (NS, NS) sector and also from the (R, R) sector, since this sector is “doubly” fermionic. The spacetime fermions arise from the (NS, R) and (R, NS) sectors.”

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type IIA

(NS+, NS+) (bosons), (NS+, R+) (fermions), (R-, NS+) (fermions), (R-, R+) (bosons)

type IIB

(NS+, NS+) (bosons), (NS+, R-) (fermions), (R-, NS+) (fermions), (R-, R-) (bosons)

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p.323 “Just like the massless states in bosonic closed string theory they carry two vector indices.”

This line implies that the phrase “bosonic closed string theory” does not refer to superstrings.

— Me@2018-04-03 10:00:13 AM

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Bosonic string theory is the original version of string theory, developed in the late 1960s. It is so called because it only contains bosons in the spectrum.

In the 1980s, supersymmetry was discovered in the context of string theory, and a new version of string theory called superstring theory (supersymmetric string theory) became the real focus. Nevertheless, bosonic string theory remains a very useful model to understand many general features of perturbative string theory, and many theoretical difficulties of superstrings can actually already be found in the context of bosonic strings.

— Wikipedia on Bosonic string theory

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What is the difference between closed string and closed superstring?

— Me@2018-04-09 09:41:18 PM

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‘Superstring theory’ is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that accounts for both fermions and bosons and incorporates supersymmetry to model gravity.

— Wikipedia on Superstring theory

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