What kind of extra force could rule out string theory?

[MTd2]

Suppose we detect a new force whose gauge group would require a SU(N) rep. What would be the smallest one that could not fit within string theory?

 

[humanino]

String theory can certainly accommodate SU(N) whatever N.

 

[MTd2]

I meant a new force. So, it could go beyond the SM, like this, U1XSU2XSU3XSU4X...?

 

[tom.stoer]

What about E(N) with N>8?

 

[suprised]

What about E(N) with N>8?

Lol, that doesn't exist. But it seems that the rank of the gauge group is limited in string theory, though no rigorous proof has been given to my knowledge. AFAIK that maximum that had been obtained (work by Candelas et al), was in the order of several 100.000.

That applies for the full theories with gravity. When gravity is decoupled, so that one talks about "non-compact" compactifications, then N can go to infinity. In other words, it appears that coupling to gravity puts constraints on the possible gauge symmetries; I wonder whether and how this becomes visible in other approaches.

 

[Kevin_Axion]

surprised, tom.stoer is referring to the Infinite Simple Lie Groups: A_n, B_n, C_n, D_n.

 

[tom.stoer]

Lol, that doesn't exist.

It does exist, but it turns out that it becomes an infinite-dimensional Kac-Moody algebra.

surprised, tom.stoer is referring to the Infinite Simple Lie Groups: A_n, B_n, C_n, D_n.

no

 

[suprised]

surprised, tom.stoer is referring to the Infinite Simple Lie Groups: A_n, B_n, C_n, D_n.

Couldn't gather that... I took it as a joke.

 

[tom.stoer]

No joke! Nicolai is working on something with E(10) and E(11). Have no idea about that; I tried to understand this Kac-Moody stuff for some time ...

 

[suprised]

It does exist, but it turns out that it becomes an infinite-dimensional Kac-Moody algebra.

Ah that you meant - well it can't exist as a gauge symmetry for which the roots correspond to massless gauge bosons.

In fact, infinite-dimensional Kac-Moody algebras and generalizations do appear in strings all the time, they accompagny gauge symmetries but the extra roots correspond to massive excitations of the gauge bosons, not massless gauge fields.

Actually the whole string spectrum (or let's be on a better defined ground: the BPS sector rather) forms a generalized lorentzian or hyperbolic algebra. But we were talking here about gauge symmetries generalizing SU(n) which are different. The algebras E10, E11 are still something different, they are symmetries of extended supergravities compactified to low dimensions, like 2,1,0.

 

[tom.stoer]

Why isn't it possible to write down a covariant derivative for Kac-Moody algebras?

 

[suprised]

The "extra" gauge fields are not massless... the structure of a KM algebra is like this: at the "bottom" there is an ordinary algebra, which correspond to the massless gauge bosons. Then there is an infinite sequence of massive "excitations" that can be thought of as a cone over this algebra. In string theory those correspond to massive excitation modes of the gauge bosons; you always get the full tower and nothing less (I had alluded to this earlier when I mentioned somewhere else that string theory is extremely finely tuned and fixed in the massive sector). This is simply because the whole thing represents a loop algebra and this is nothing but the stringy generalization of gauge symmetry.

Strings would be disproven by finding that this tower is not there.

What you seem to ask for is a setup where all the infinitely many roots would correspond to massless gauge bosons. That is obviously a sick gauge theory.

On the other hand, why should one consider only standard gauge theories. There are other field theories one could associate with exceptional algebras, like conformal fixed points or non-critical tensionless strings. And indeed, by tuning singularities in string compactifications one can obtain not just standard QFT's in the low energy limit but also strange theories.

 

[tom.stoer]

The "extra" gauge fields are not massless... the structure of a KM algebra is like this: at the "bottom" there is an ordinary algebra, which correspond to the massless gauge bosons. Then there is an infinite sequence of massive "excitations" that can be thought of as a cone over this algebra. In string theory those correspond to massive excitation modes of the gauge bosons; you always get the full tower and nothing less (I had alluded to this earlier when I mentioned somewhere else that string theory is extremely finely tuned and fixed in the massive sector). This is simply because the whole thing represents a loop algebra and this is nothing but the stringy generalization of gauge symmetry.

This is just the situation is string theory; I understand.

What you seem to ask for is a setup where all the infinitely many roots would correspond to massless gauge bosons. That is obviously a sick gauge theory.

Yes, this is what I am asking; why is such a theory sick?

I mean - yes - you would create infinitly many massless degrees of freedom, but perhaps you can generate infinitly many constraints as well and get rid of some degrees of freedom; look at the center symmetric phase in QCD where the theory somehow reduces itself to the center of the gauge group (don't take this too literally :-)

 

[suprised]

I mean - yes - you would create infinitly many massless degrees of freedom, but perhaps you can generate infinitly many constraints as well and get rid of some degrees of freedom; look at the center symmetric phase in QCD where the theory somehow reduces itself to the center of the gauge group (don't take this too literally :-)

Well a theory with infinitely many massless gauge fields seems a bit pathological, isn't it ... It isn't exactly what one would aim for when trying to describe the standard model...but indeed, anyone is cordially invited to study such theories ;-) Putting constraints to remove the infinitely many states seems like going back to a well-defined starting point, which one could have chosen to start with in the first place.

No one can exclude the logical possiblity that our world corresponds to some very non-standard QFT (non-critical strings, conformal fixed points) with exotic properties, whose IR limit looks for some reason as the standard model. The question is how well-motivated such ideas are, usually the "anything goes" approach doesn't lead to anywhere.

 

[MTd2]

So, there is no gauge theory that cannot be described by string theory at some limit, right?

 

[tom.stoer]

So, there is no gauge theory that cannot be described by string theory at some limit, right?

This is the swampland-discussion.

 

[MTd2]

But humanino said it could accommodate for any SU(N)...

 

[humanino]

But humanino said it could accommodate for any SU(N)...

I have not read about those in a while, but I do remember explicit brane stacking constructions of SU(N) were consistent. I should check when I come home, but it seem to me this is also in Zwiebach's book.

 

[suprised]

So, there is no gauge theory that cannot be described by string theory at some limit, right?

But humanino said it could accommodate for any SU(N)...

Read carefully what was written … if you decouple gravity, for example if you consider the gauge theory that is seen by placing yourself on the world-volume of a stack of D-branes, then arbitrary N is possible. This is also what the usualy AdS/CFT correspondance is talking about. It is what I called a "non-compact compactification" (well I admit this can't be understood without lots of explanations).

The question is whether you can do this in the full theory including gravity. And the anser seems no. You can't put an arbitrary number of branes or fluxes in the theory because in a true "compact" compactification, the flux must go somewhere. This is a "global" constraint that ultimately arises when you like to consistently couple the theory to gravity.

So these stacks on N D-branes that are seen everywhere are to be seen as models for gauge theories only, where one pretends as if there wouldn't be any constraint coming from the coupling to gravity. These constraints are global in the sense that you can't see them by just looking locally to your stack of D-branes. Unfortunately you won't find such subtleties in introductory texts.


And indeed, all these questions touch right at the heart of the swampland problem.

 

[MTd2]

What I have in mind is an extra force, not just getting an SU(N). Forget about gravity now. So, in fact I am saying

Standard Model X SU(N).

Well, one second thing. A standard model X SU(N), coupled with gravity, what would be the smallest N to fall inside the swampland?

 

[MTd2]

You can't put an arbitrary number of branes or fluxes in the theory because in a true "compact" compactification, the flux must go somewhere. This is a "global" constraint that ultimately arises when you like to consistently couple the theory to gravity.

Sounds like there is some sort of p-1-form electromagnetic potential from every p-brane. Where does the flux go and what is the constrain?

 

[MTd2]

I tried to read about fluxes in m theory, but I couldn't keep what I read in my mind. Perhaps discussing here will help me, ok?

Is this something nice:

http://www.physics.rutgers.edu/~gmoore/IHES_TalkI_v2.pdf

 

[suprised]

I tried to read about fluxes in m theory, but I couldn't keep what I read in my mind. Perhaps discussing here will help me, ok?

This is a good rewiev article:

http://arxiv.org/pdf/0803.1194

 

[tom.stoer]

very simple question: is there a generalization of the formula U = exp(iA) where A is an element of a Kac-Moody algebra and U defines some generalized symmetry transformation?

 

[LukeD]

Personally, I hope that there is no force or particle that could not be accommodated by String Theory. See, I have high hopes for its mathematical -if not physical- significance.

There's even a stringy proton right? A single string that approximates the properties of a proton.