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I've just learned from this one of Prof. Wen's answers that there exists a theory called string net theory. Since I've never heard about this before it picks my curiosity, so I`d like to ask some questions:

How is string net theory related to the "usual" string /-M-theory framework? I mean if there is a relationship between them ...

Are the strings in string net theory and in string / M-theory the same?

What are the differences in the goals one wants to achieve or phenomena in nature one can describe with those two theories?

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up vote 11 down vote accepted

Goals one wants to achieve with those two theories are similar.

We know that superstring theory is a potential theory of everything. One may want to ask what is the difference between the string-net-liquid approach and the superstring approach? Our understanding of the superstring theory has been evolving. According to an early understanding of the superstring theory, all the elementary particles correspond to small segments of superstrings. Different vibration modes of a small superstring result in different types of elementary particles. This point of view is very different from that of the string-net liquid. According to the string-net picture, everything comes from simple qubits that form the space. No qubits no space. The "1" qubits form string-nets. The strings can be as long as the size of universe, which fill the whole space. Light (photons) correspond to the collective motion of the large string-nets and an electron corresponds to a single end of string. (See a picture of string-net "vaccum". See also a talk) A modern understanding of the superstring theory is still under development. According to Witten, one of the most important questions in superstring theory is to understand what is superstring. So at this time, it is impossible to compare the modern understanding of the superstring theory with the string-net theory. In particular it not clear if the superstring theory can be viewed as a local bosonic system (ie a qubit system). The string-net theory is fundamentally a local bosonic system (ie a qubit system).

So, if superstring theory is a qubit model (or a quantum spin model in condensed matter physics), then superstring theory and the string-net theory is the same, since the string-net theory is a qubit model (or a quantum spin model in condensed matter physics).

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Thanks for these nice explanations, it already helps. Before Ill gonna watch the slides of the talk, there are some further things Im not sure if I get it right: conserning the qubits of value 1 that make up space, are they some kind of excitations of the spin net too? When you say photons are excitations of collective motions of the string net (?), is this true for all of the bosons in the theory? The part with the electrons (and other fermions too?) that correspond to a single end of a string I dont understand yet. Are they attached at the ends – Dilaton May 27 '12 at 17:34
...(similar as the querks in the string model for meson scattering) or do the electrons (and other fermions) correspond to the motion of just the respective endpoint? BTW is string net theory supersymmetric too and what number of spacetime dimensions is needed to formulate it consistently? Ok, now I better gonna watch the slides :-) – Dilaton May 27 '12 at 17:37
The space is made of qubits of value 1 or 0. The string is formed by qubits of value 1. The ground state is a superposition of all string-net configurations, which is particular quantum entangled state of qubits. The collective excitation of this particular entangled many-qubit state happen to be light. The end of string correspond to a topological excitations above the ground state which correspond to electrons. Any gauge charged particle correspond to string ends, bosons or fermions. String-net does not have to be supersymmetric, and lives in any dimensions. – Xiao-Gang Wen May 27 '12 at 18:13
Doesn't that mean that string-net theory is lorentz-violating? – centralcharge Jun 29 '13 at 9:05
@Dimension10: Yes, string-net theory is lorentz-violating in general. – Xiao-Gang Wen Jul 26 '13 at 23:39

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