# Are string theories gauge theories?

The wikipedia page for String Theory lists $\text{SO}(32)$ and $\text{E}_8\times \text{E}_8$ as group symmetries of some of the string theory types, and the page on $\text{E}_8$ says:

$\text{E}_8\times \text{E}_8$ is the gauge group of one of the two types of heterotic string

Am I to infer from this that these string theories are "gauge theories" (I guess "string gauge theories" rather than "QFT gauge theories"), or am I missing something? I certainly can't find any literature that ever calls String Theory a "gauge theory".

• Define gauge theory (I think it's subjective) and we'll see then. – Chris Gerig Mar 25 '13 at 18:11
• @Chris Gerig, well, I would say it would mean that adding a requirement of local invariance under some continuous symmetry group implies the necessary existence of some compensating field or stringy-feature that gives rise to dynamics.... – user1247 Mar 25 '13 at 19:47

In almost of its $d=4$ vacua, string theory contains Yang-Mills degrees of freedom or light spin-one particles so that in the form of the string field theory, it may be rewritten as a field theory with a gauge group, a generalized Yang-Mills theory with infinitely many fields charged under the gauge group. The gauge symmetry is exact in this formulation because it's what removes the unphysical polarizations of the gauge fields.

However, string theory is not a local quantum field theory and the gauge symmetry isn't a fundamental assumption in string theory – it and the corresponding polarizations of the gauge bosons are derived from something more fundamental, from the maths of string theory (e.g. from conditions of the world sheet conformal field theory if we deal with the string theory perturbatively). General relativity also follows from string theory (much like Yang-Mills theory, the diffeomorphism invariance is exact whenever we rewrite string theory in a form that includes $g_{\mu\nu}$ as the degrees of freedom) but it's a derived result, an infinitesimal glimpse of the superior power of string theory.

It's hard to answer your question because the phrases you use are ill-defined – in particular, you don't say whether a gauge theory has to be a local quantum field theory in spacetime (string theory is not one). But I believe that the paragraphs above answer all meaningful questions that one could get by clarifying yours.

There is an interesting article written on the relationship between the two (it is actually a workshop) which you may find interesting

http://www.mathnet.ru/php/conference.phtml?confid=335&option_lang=eng

One issue in mathematics and physics is the separation of the two - people working in physics aren't always up on the latest maths, and vice versa. Same goes with competing physics theories.

Quote "The first workshop is devoted to the aspects of interrelations of String Theory to Gauge Theories and comparing of physicists' and mathematicians' viewpoints"

One of the videos (there are many in this workshop) discussing similarities is this introduction: http://www.mathnet.ru/php/presentation.phtml?option_lang=eng&presentid=5227

• Good answer, but it would be better if you would paste the essential parts of the references here. It is important, because in the case of the link rotting, or if the googlers of the future won't click any more, they could also understand what you wrote. – peterh Aug 3 '16 at 16:47