Perhaps the string people here (or anyone else) will have come across something about this. There's a gravity/gauge duality in Type IIA and IIB and its also known to occur in M theory, though much less understood. You can, via T, S and U dualities, get from Type II constructions to heterotic ones so I would vaguely expect there to be some kind of heterotic gravity/gauge duality. My supervisor can't think of one but reckons anything with branes should have it, even if they are much outside our common experience but perhaps there's something to do with the heterotic nature of the theories which prevents them or obscures such a formulation. Anyone know of any? There's a few methods of construction I would hazard would be possible, Type IIB -> Type I -> SO(32) via orientifolding and S duality, some kind of S or U dual of Type IIA, Low energy limit of a compactified M theory -> \(E_{8}\times E_{8}\) or the direct route of construction within heterotic theory itself. I've Googled and ArXiv'd a bit but nothing jumps out at me. Anyone got any experience with it, even in passing?

Hey Alpha--- I've worked pretty exclusively with the heterotic string (weakly coupled), and have never heard of anything like this. This was an idea that I kicked around to a few post docs that I've worked with, and I'll have to think about the eventual reason that it didn't work.

In usual formulations the gauge theory is put on the boundary of the non-compact space and in M or Type II theories this is not a problem as you have AdS space but I suppose in heterotic you have the usual of different left and right mode dimensionalities. I'll admit, other than knowing they exist, knowing their T and S duals and having seen their massless Lagrangians I couldn't tell you much else about heterotic models so I'm not sure if the 10/26 string modes is a problem or not. The derivation of AdS space in Type IIB from a stack of D3 branes (or any other Dp stack in Type II) is given in Schwarz and Becker and its pretty straight forward. I have no idea how I'd generalise that to heterotic strings but surely stacking a bunch of branes in heterotic models gives you some kind of space-time layout defined by the stack, even if the issue of a gauge dual is unclear?

This isn't something I've ever heard of. The only string duals I'm aware of are to Type IIB, IIA and M theory (as you said). I'll ask around the department when I'm in next.

Having just googled around I've found a paper which mentions that the Type IIB D1-D5 space-time is \(AdS_{3} \times S^{3} \times T^{4}\). By T duality you can get to Type IIA. By orientifolding you can get to Type I. By S duality you get to Type IIB but with F-strings doing the D-string job. If you can get to Type I then you can S dualise that to SO(32) heterotic and then T dualise to get to E8xE8. If no one has done that then I'd imagine there's something not good about orientifolding the gauge theory. Breaking N=2 to N=1 in Type IIB using D7 branes makes the gauge theory pretty unpleasant so doing it by some kind of abstract method like orientifolding would probably be worse. And there's somethign funny about the Type IIB -> Type I relationship because Type I doesn't inherent Type IIB's self S dual nature but I don't know enough about Type I to know why....

The most naive answer has got to be that there are no simple heterotic branes. Stacking branes is the traditional route to AdS/CFT, but heterotic strings don't have branes to stack. What's the state of the art in open heterotic strings?

Heterotic string theory has branes. You can define branes in bosonic string theory and since it exists, in some form, in all the supersymmetric string theories branes are in all of them. I don't see much about the space-time structures of heterotic string theories in the literature compared to Type II constructions. Heterotic papers or sections in book tend to stick with gauge group stuff instead.

Sure, I didn't say heterotic didn't have branes, I said it didn't have simple branes. Haha, I do stand by the adjective simple. Especially if one is inheriting those branes from the bosonic string.

From the field theory side, I have a hard time imagining what sort of field theory would fit the bill. Especially when doing semi-classical or classical computations on the gravity side. For example, how should I interpret the classical configuration of a hetorotic string ending at two points on the boundary?

Nope, I have no hidden technical assumptions. In my opinion heterotic branes are just more complicated than simple IIA/B D-branes, that's all. I don't think that's a terribly controversial statement. I think IIA/B D-branes are less complicated than bosonic string branes because they are more stable. Do you agree? Note added: I do think you could make my statement technically precise if you wanted to. And I'm definitely not saying it's impossible. I am definitely not an expert on this topic! All I meant to say is that if you're playing things "fast and loose" then there is a simple heuristic reason why heterotic AdS/CFT would have to be a bit strange.

The brute force and ignorance approach to this would be to write down the Lagrangian of the supergravity limit of the heterotic string and doing Maldacena's analysis to see what happens. I don't know if the SUGRA limit of the heterotic string is nice to look at or even exists though...

The heterotic string has a very nice SUGRA limit, thank you very much Please Register or Log in to view the hidden image! It is E8xE8 (N=1) gauge theory in 10 dimensions, at least in the weak coupling limit. This may be part of the problem, as the guage theory from heterotic strings comes from a qualitatively different place. The branes in the type II theories give you gauge theories, whereas the gauge theory from heterotic strings is somehow ``innate''---it comes from the dimensional reduction in the bosonic sector. Alpha eluded to this originally.

Very refreshing, and interesting, to see a genuine discussion about modern physics on this forum. Nice work chaps! Sadly, I have no idea what you're all talking about! Please Register or Log in to view the hidden image!

I'm afraid my experience of strings are pretty limited to the type I and II strings so I wasn't even sure that this would be true. To be honest, I wasn't sure what the heterotic string was at all until I looked it up after reading this topic. Please Register or Log in to view the hidden image! I feel I'm repeating what others have previously said (again) but the lack of a nice gauge theory interpretation of branes will make life pretty difficult from the point of view of interpreting what the gauge theory dual of a heterotic supergravity solution is. That's not to say that there is no interest in this topic from my point of view - there are plenty of papers where people describe gravity solutions in type II theories where the dual field theory is unknown, or one can only guess at the properties of it by doing holographic calculations.

The dual field theory may not even be a gauge theory. I think all we really know about it is that it should possess at least an \( E_8 \times E_8 \) global symmetry, if the usual rules of AdS/CFT hold.