# Is String Theory a Field Theory?

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.

• Yes, it is a field theory of a non-point-particle. Commented Jun 13, 2012 at 6:30
• From what I gather in en.wikipedia.org/wiki/… , string theory includes/explains qft . Commented Jun 13, 2012 at 8:20
• It is not a field theory--- it does not have local fields at space-time points. Commented Jun 14, 2012 at 0:47
• What do you call string fields? Commented Jun 19, 2012 at 17:55
• @ErnestoUlloa: String fields are nonlocal, they are not defined at space-time points. Commented Jun 19, 2012 at 21:01

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.

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.

• I deleted some inappropriate comments here. Those involved are free to continue the discussion in Physics Chat, but not here. Commented Jun 20, 2012 at 21:13

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

• 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. Commented Jun 20, 2012 at 12:42
• 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. Commented Jun 20, 2012 at 17:27
• 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. Commented Jun 20, 2012 at 17:29
• 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 Commented Jun 20, 2012 at 17:48
• 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. Commented Jun 20, 2012 at 20:16