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I figure that string theory is a new breed of QFT which looks at fields in terms of a network of strings and also incorporates gravity into its module, however my question is that since elementary particles can be thought of as excitations in a field in QFT and likewise particles can also be thought of as vibrating strings in String theory, does this mean that the strings in String theory are actually troughs (like in waves) in there corresponding fields?

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    $\begingroup$ Your initial assumption is a long way wide of the mark. $\endgroup$ – John Rennie Oct 29 '14 at 6:14
  • $\begingroup$ @John Rennie-Hello John, U mean the assumption that strings are like fields or that that string theory is a new breed of QFT, I'm curious as to the specific flaw in my question? $\endgroup$ – GammaRay Oct 29 '14 at 7:25
  • $\begingroup$ I can't comment with any authority since I've only read introductory string theory stuff. However it is entirely unlike quantum field theory. It is one of the miracles of string theory that QFT emerges as a long range/low energy limit. So your question is basically meaningless. Sorry. $\endgroup$ – John Rennie Oct 29 '14 at 7:53
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    $\begingroup$ @JohnRennie there do exist corresponding diagrams to the Feynman diagrams of QFT though.benjaminjurke.net/show/string-theory $\endgroup$ – anna v Oct 29 '14 at 9:03
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I figure that string theory is a new breed of QFT which looks at fields in terms of a network of strings and also incorporates gravity into its module,

You should read some reviews of what string theory is .

String theory rejects the idea of a point particle as the fundamental constituent of the theory, which is the central concept in quantum field theory. By introducing 1-dimensional, extended objects (and higher dimensional membranes in its further developments) this gives rise to a natural smallest scale in form of the string length.

The average size of this string is expected to be much smaller than the smallest sizes probed experimentally, currently 10^(−16) centimetre, and might be as small as the Planck length, which is of the order of 10^(−33) centimetre.

So when one studies string theory at low energies compared to the Planck scale, it becomes difficult to see that strings are extended objects—they behave effectively 0-dimensional, i.e. pointlike. With this perspective in mind, point-like quantum field theory can be regarded as a sort of effective theory for strings at low energies.

Italics mine.

however my question is that since elementary particles can be thought of as excitations in a field in QFT and likewise particles can also be thought of as vibrating strings in String theory, does this mean that the strings in String theory are actually troughs (like in waves) in there corresponding fields?

No, because, as the quote says above, the QFT particles are the limit of the strings at low energies . The corresponding fields are String field theories which are

a formalism in string theory in which the dynamics of relativistic strings is reformulated in the language of quantum field theory. This is accomplished at the level of perturbation theory by finding a collection of vertices for joining and splitting strings, as well as string propagators, that give a Feynman diagram-like expansion for string scattering amplitudes.

Creation and annihilation operators, which are used in QFT exist also in string field theories, it is just that instead of point particles one has one dimensional strings, so this idea of troughs is no go.

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