Realistic string theories must contain fermionic states, like the states of electrons or quarks. Superstrings include anticommuting dynamical variables in addition to the commuting coordinates Xµ that describe the position of strings. For open superstrings, quantization gives a state space with a Neveu–Schwarz (NS) sector that contains bosonic states and a Ramond (R) sector that contains fermionic states. The theory has supersymmetry, a symmetry that ensures that the number of bosonic and fermionic degrees of freedom are the same at any mass level. We examine type II closed string theories, which arise by tensoring the state spaces of open superstrings.
Introduction
We have so far studied bosonic string theories, both open and closed. These string theories live in 26-dimensional spacetime, and all of their quantum states represent bosonic particle states. Among them we found important bosonic particles, such as the photon and the graviton. Non-Abelian gauge bosons, needed to transmit the strong and weak forces, also arise in bosonic string theory, as we will see in Chapter 15.
Realistic string theories, however, must also contain the states of fermionic particles. You may recall that a quantum state of identical bosonic particles is symmetric under the exchange of any two of the particles. A quantum state of identical fermionic particles, on the other hand, is antisymmetric under the exchange of any two of the particles. Quarks and leptons are fermionic particles. To obtain them we need superstring theories.
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