# Is the String Field of String Field Theory the same (ontologically identical to) as the field of QFT?

Disclaimer: Although my maths is quite good and I have a background in computer science and software engineering, I am a philosopher specialising in information theory (and what is called the philosophy of information) so please be kind if you can. I am terribly nooby and may say dumb things.

I have read John Gribbin's Not Even Wrong, this neato blog, I have had a look at this post, and this one, and this one. (and this)

I have a very basic understanding of the concept of first and second quantised theories. I also more or less get the following (see the disclaimer above):

1. M-Theory is the current best version of string theory, having been unified from several (five - I think) separate string theories by Whitten in the late 1980s
2. There is ample physical/experimental evidence in support of QFT and the quantum field, but not very much at all for String theory and its membranes.
3. The quanta of QFT are excitations in (emerging from) the quantum field, and these are the (reductive) basis of the existence of the different particles of the standard model of quantum/particle physics
4. Strings are not quanta qua/per QM and QFT: they are mathematically and presumably ontologically (this goes to my question) different beasts
5. Membranes might intersect (M-Theory) with membranes in other universes, providing a physico-mathematical formalism that accommodates many worlds interpretations of QM (I think - I am not too sure about that)
6. String theory is apparently very mathematically elegant with respect to representing/modelling many phenomena

Now. I realise that there are a lot of mathematical constructs deployed in QM and QFT and that there are debates relating to such things as interpretations of QM about which ones correspond to physical entities (like operators for example) in the actual mind, mathematics, and language independent physical/material natural world that is the subject of investigation in experimental physics (i.e. - the physical universe or multiverse depending on which one we turn out contingently to be living in).

I also understand that string field theory is much less developed than quantum field theory. However, when I try to get a quick concept of how the string field relates to the quantum field ontologically, I end up facing what seem to be contradictions (which I am sure are largely down to my ignorance.)

For example - there is a book available (which book is probably fantastic - I have not read it) the title of which is "Quantum Field Theory of Point Particles and Strings (Frontiers in Physics)" and for which the abstract says:

The purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of the quantum field theory and provides for a coherent development of the generalization and application of quantum field theory for point particles to strings....The book is unique in that it develops all three representations of quantum Field theory (operator, functional Schrödinger, and path integral) for point particles and strings. In many cases, identical results are worked out in each representation to emphasize the representation-independent structures of quantum field theory.

So it's clearly the case that many mathematical apparatus deployed in QFT can be deployed for string field theory. HOWEVER - is this supposed to correspond to the identity of the fields referred to by the two theories in the physical ontology of the natural world (each theory has a theory-ontology: do both map to the same external physical ontology w.r.t the field of each)?

Moreover, the Wikipedia page about string theory starts thus: "String field theory (SFT) is a formalism in string theory in which the dynamics of relativistic strings is reformulated in the language of quantum field theory."

Note that it says "language of quantum field theory", which leads me to believe it is probably a text to get QFT theorists to understand string theory and the string field using language they understand.

So my dumb question boils down to this: is the field of string field theory (meant to be identical to) the quantum field in ontological terms?

Presumably, string theorists and QFT physicists are ultimately shooting at the same ontic and explanatory objective, but then (and remembering that I understand basically there are arguments about the interpretations of QM and their ontological commitments) string theorists say stuff like:

However, string theory is not a quantum field theory, and this shows In the "stringy Feynman diagrams" it used to compute perturbative string amplitudes. Here, one might start to think that the string becomes analogous to the particle because the diagrams simply are two-dimensional manifolds that look like "fattened Feynman diagrams", with string interaction corresponding to higher-genus 2D manifolds.

And they say stuff like:

To start addressing this question I will first say that while I think that string theory has something to do with fundamental physics I do not particularly see it as all (strings uber alles) but as something which may reflect a pattern in the structure of reality.

Presumably, both fields have to account for the ample experimental evidence proving the existence of many (all?) of the particles of the standard model, and presumably, both have to accommodate the vacuum (which seems to be ontologically primitive in QFT). Or - maybe not??

Another way of putting my question is as a T/F:

The string field and the quantum field of SFT and QFT respectively are (taken to be/represent) the same field in the physical world but modelled using very different mathematical constructs: True or False? Why?

• String theory is not a field theory: physics.stackexchange.com/q/30007. And related
– user154420
Jun 25, 2017 at 13:30
• This doesn't in fact answer my question. That I understand that string theory is not a quantum field theory (which I understand is based on the fact that it was initially posited as an alternative to QM and strings are an alternative to quanta as 1st quant. ) should be obvious if you have read my question. There IS however, a string field theory. My question is rather - if there is a string field theory (which there IS) as well as a quantum field theory (which of course there is) - then is the real world field referred to in QFT meant to be the same physical field as that of SFT, or not? Jun 26, 2017 at 1:24
• So my dumb question boils down to this: is the field of string field theory (meant to be identical to) the quantum field in ontological terms? Please regard this as a cautious response from a person with a sketchy knowledge of the math behind each approach. My novice/simplistic understanding to your "dumb" question in bold above is NO. String theory does allow for the incorporation of gravity, making it (potentially) a more complete description of what the universe "really" is, whereas QFT has, to my knowledge, never attempted to include gravity.
– user154420
Jun 26, 2017 at 2:03
• As far as Wikipedia goes, it is constantly edited, so contentious subjects are constantly rewritten, so I would not be relient on it. If you search through the site for questions similar to yours, I think you will find as many comments and answers regarding the question" is string theory a field theory" in the affirmative as in the negative, although my sincere apologies for rushing to impose a definite border between the two theories, I simply don't know physics well enough to arbitrarily impose such a distinction.
– user154420
Jun 26, 2017 at 2:22
• @Countto10 OP specifically referred to "string field theory", which is one particular formulation of string theory. It looks like that your comments miss the point. Jul 5, 2017 at 6:02

The fundamental operators in quantum field theory are associated with individual points in space-time; for example, the annihilation and creation operators for the various particle species.

The fundamental operators in string field theory are associated not with points, but with one-dimensional paths in space-time. There is e.g. a creation operator for each possible string configuration, the effect of which is to "add one string" in that shape and location.

Interactions of quantum fields are represented by products of quantum field operators at the same point. Interactions of string fields are represented by products of string field operators which touch at some point.

So there are strong similarities, but also differences.

It is said that you can re-express string field theory as a theory of infinitely many quantum fields. There would be a quantum field for each of the excited states of the string, that appear in the quantum theory of the individual free string, and then you would need to re-sum the string field interaction terms, in terms of pointwise interactions of these quantum fields. (I don't have a reference for this, but it makes sense.)

You may see further comments about string field theory, from a real string theorist, here. (Note that it's not the blog post, but a comment below, that I am linking to; you have to wait a while for it to load.) He remarks that string field theory is probably not the fundamental language of string theory, precisely because it privileges strings over branes; it's just another way to motivate the sum over string histories that defines perturbative string theory.

• As a minor comment, defining QFT as "associating fundamental operators to spacetime points" is a narrow definition of QFT. It may work for a "local QFT of point-particles", but nothing prevents defining a QFT of extended objects (strings or general branes), non-local operators, etc. May 4, 2023 at 21:43