# Is String Theory a Field Theory?

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Is String Theory a Field or Quantum Mechanical Theory of the String rather than a Particle?

I should know this having studied this for a term, but we jumped into the deep end, without really covering the basics of the theory.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Mozibur Ullah

asked Jun 13, 2012
edited May 11, 2014
Yes, it is a field theory of a non-point-particle.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Chris Gerig
From what I gather in en.wikipedia.org/wiki/… , string theory includes/explains qft .

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user anna v
It is not a field theory--- it does not have local fields at space-time points.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ron Maimon
What do you call string fields?

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ernesto Ulloa
@ErnestoUlloa: String fields are nonlocal, they are not defined at space-time points.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ron Maimon

## 4 Answers

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String theory isn't a quantum field theory. See What is the stress-energy distribution of a string in target space? and Statistics and macrolocality in string theory. See Do we need a quantum deformation of the diffeomorphism group in string theory? for a contrary opinion.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Kupla
answered Jun 13, 2012 by (30 points)
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According to the definition, a field assigns a value (classically; or a distribution quantum mechanically) to every point in the space(-time). So field theory deals with point-like excitations in the space(-time). String theory, thus, is not quite a field theory, since it's excitations are defined on extended objects. To better understand the difference, I would look at http://en.wikipedia.org/wiki/String_field_theory. Also, another important difference to notice is that people consider a few fundamental particles interacting with each other when they do qft; however, in string theory there are an infinite number of fundamental excitations in the theory, leading to an infinite tower of fundamental particles.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Kachal
answered Jun 13, 2012 by (0 points)
I deleted some inappropriate comments here. Those involved are free to continue the discussion in Physics Chat, but not here.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user David Z
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In string field theory a string field creates string excitations from the vacuum that interact. Interactions are treated using perturbation theory. The theory uses string vertex operators and string propagators. SFT is definitely a quantum field theory, but not a point particle QFT. It is used mostly in the study of unstable branes, topological string theories and non-commutative geometry. The principal versions of SFT are Light-Cone SFT, Covariant BRST SFT & Witten’s SFT. In principle string theory should be formulated as a quantum field theory of strings, but due to technical reasons related to the difficulties inherent to the above string field theory formulations, or simply by the incomplete knowledge of the underlying theory, that most calculations in the string theory literature are done in the context of first quantized formulation or in low energy effective classical actions. So it can be said that string theory & M-theory are, in principle, quantum field theories for extended objects, even if calculations are not generally done in this formalism

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ernesto Ulloa
answered Jun 19, 2012 by (30 points)
It is not a field theory, because the string field is nonlocal. The formulation is also problematic.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ron Maimon
Ron, again you are confused, because the question was not if string theory was local or not, it was if string theory is a quantum field theory or not. The original question was not about locality.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ernesto Ulloa
Ron, maybe you we have to think about the term "Field" in a more general term that what mathematicians call field. Locality is a concept that is rooted to the very postulates that define most of our concepts of real analysis. A mathematician will almost always define a field as a local function of space. There is not a calculus based in functions that are non local functions of x,y,z. You have to extend your notion of what is a field. My earlier comment was a little bit rude. I apologize.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ernesto Ulloa
You never have to apologize to me for rudeness! The term "field" requires that there are operators which commute which attach to each space-time point. This microcausality is the absolute irreducible minimum requirement for calling something a field theory. The string fields do not make microcausal anything, and the string theory does not have local fields. It's S-matrix theory, not field theory.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ron Maimon
Why dont you say that to Edward Witten the Field Medal winner in mathematicas, because he also call String Field Theory a QFT of strings. Your arguments are just not relevant.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ernesto Ulloa
Witten already knows this. String field theory is a "field theory" of strings in the sense that it gives second quantized operators for creating and annihilating strings. It is not easy to define the formalism, it was originally for light-cone gauge only, although there are certain covariant formulations. It is not like fields in field theory, which have their own consistent path integral and give a consistent microcausal definition to the particles. It is a massively nonlocal field theory, where the fields are defined on loops.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ron Maimon
I'm afraid you dont know about Witten's formulation of string field theory. Read the papers.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ernesto Ulloa
Witten's string fields are not microcommuting local fields, but fields on loops. There are no microcommuting local operators at space-time points in the theory. This makes it different from QFT. I don't need to read anything--- there are no local fields in string theory, because there are a different number of degrees of freedom at short distances than in field theory. The infrared ultraviolet duality means that high energy strings are big, not small, so there isn't a local notion of stuff at a point.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ron Maimon
Ron, read the original question. It was not asked anything that you have commented is just that your conditions for not calling it quantum field theory are not relevant. I think that your point is that SFT is not an ordinary field theory (causal, local, etc.). But if you think about it you are arguing that it is complicated, or that is not causal, but the original question was a simple one. You are complicating the original question. Thanks for telling me that I don't need to apologize, this way I can speak frankly.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ernesto Ulloa
Every Quantum Theory with Fields is a QFT. You are confusing terms. You are talking know about divergences wow! This has nothing to do with this.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ernesto Ulloa
I am not confusing anything. Not every theory with fields is a QFT. If your fields live in loop space (the space of all curves on a surface) and not on the space itself, then they aren't attached to points. The "divergences" is important--- a field theory has independent degrees of freedom at every point and this is what gives rise to the divergences. It is also why string theory can't be formulated using local fields, only using loop fields. Loop fields are not local fields, and this is important to say, so that no string field theory is a field theory proper. I think we are arguing semantics

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ron Maimon
But the semantics are important still. How can you call something which does not have degrees of freedom at a point a field? For me, the prerequisite defining property of a true field theory is that you can attach observables to points. String fields are at best analogous to local fields, not an example of local fields. Speaking frankly is good, by the way! At least I get where you are coming from quickly.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ron Maimon
Ron, you are just missing the point. You just said it. In your own words you just said "For me, the prerequisite defining property of a true field theory is that you can attach observables to points" , so this is clearly your opinion.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ernesto Ulloa
That why you claim to be the next Newton! You are complicating the original question so readers accept your opinion by obscuring the original argument with irrelevant fanciness. Your statement of something that has no degrees of freedom is completely false.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ernesto Ulloa
String fields create and destroy quantum string states in physical spacetime. It doesn’t matter if SFT have problems, or if its non local of anything else. It is a quantum field theory of strings. You can read about this in Siegel’s introduction to the subject insti.physics.sunysb.edu/~siegel/sft.pdf.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ernesto Ulloa
If you aren't attaching observables to points, what do you mean by "field"? There is no other sense I know. I am not going to read, I know what string field theory is, and it is not particularly fundamental and not particularly complete as a formulation (where's the branes?). It is usually used as a political sledgehammer people use to intimidate people, since it is technically challenging. String field theory is not much more than a rewrite of string perturbation theory. Regarding my bio, physics doesn't need another Isaac Newton, it already has Newton.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ron Maimon
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Is the string operator creating/annihilating a winding mode with winding number +1 a local operator for the case of space compactified over a circle?

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user jubla
answered Oct 3, 2012 by (-10 points)
No it isn't. This is most obvious in T-duality, where these modes switch with the ordinary string modes. This doesn't answer the question exactly (except through the Socratic method--- perhaps this was the intent), and it should be expanded to make it non-Socratic.

This post imported from StackExchange Physics at 2014-04-05 16:32 (UCT), posted by SE-user Ron Maimon

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