Monday, September 08, 2014

Vafa: supergroups, non-unitary cousins of CFT, and black hole puzzles

Cumrun Vafa has a very interesting new paper,
Non-Unitary Holography
You may start with a simple question. What happens if you replace gauge groups derived from \(U(N)\) by their supergroup counterparts, \(U(N+k|k)\)?

Well, the supergroup has more degrees of freedom – many of those have a negative norm (anticommuting but spin-one components of the "gauge bosons") and may produce negative probabilities. But Cumrun says that it doesn't affect anything you encounter at any order of the perturbative expansion in \(1/N\) i.e. in the string loop expansion. The effect of the extra \(k\) bosonic dimensions added to the original \(N\) is cancelled against the new \(k\) fermionic ones.

If true, this statement itself is surprising, at least to me (even though I know that such an addition of fermionic+bosonic dimension pairs is inconsequential in some topological theories).

So Cumrun's thesis is that the perturbative parts of theories such as the most intensely studied example of the AdS/CFT correspondence, one involving the \(\NNN=4\) gauge theory in four dimensions, heavily underdetermine the theory. At the non-perturbative level, there is a significant ambiguity about what the theory does, at least if you allow the Hilbert space to become indefinite at some point.

This may be bad news or good news. Cumrun also says that in these "evil cousins" with supergroups as gauge groups, there may exist worlds in which Stephen Hawking was (originally) right about the information loss. The evolution may be non-unitary.

These issues should be settled soon but I am confused about some statements made by Cumrun. First, there are different aspects of "unitarity". The word often means that we demand a positively definite Hilbert space – which is not the case here. But it also means that a bilinear (more accurately: sesquilinear) form is being preserved. These are independent conditions. Spaces with pseudounitary symmetries violate the former condition but obey the latter.

Another question is whether these non-unitary theories are sick or "in the swampland". I would tend to say "Yes" – it is OK for you to dismiss them entirely. But there may be ways to get meaningful theories out of them – theories with non-negative probabilities. If all the predictions are the same as in the "totally healthy" theories to all orders of perturbation theory, it's already pretty dramatic.

What I also have in mind is the possibility that some theories with ghosts may be made either exactly consistent or consistent up to a very satisfactory accuracy which could justify their usage in physics.

And of course, Cumrun spends significant time with the black hole puzzles. The matrix models are, to a large extent, physically equivalent to black hole physics (at the quantum level) so one should be able to learn a lot of things about the quantum dynamics of black holes from these considerations, too.


  1. Is the temperature inside a black hole zero?

    Does a black hole turn matter into dark matter?

    Does this dark matter abide in 3+n dimensions.

    Is it entangeled and just a huge atom of dark matter.

    Is distance in extra dimensions quantized or rolled up?

  2. This reminds me that the CFT in the Vasiliev-gravity dS/CFT of Anninos, Hartman, and Strominger is only "pseudo-unitary" too.

  3. Salute!

    Gauge groups/black brane architectures/automorphic forms derived from U(N) and gauge groups/black brane architectures/automorphic forms derived from U(N + k|k) are U-dual.

  4. Ohm actually, thanks a lot for having reminded me about that.

    Adding D-branes formally indeed adds the fermionic Chan-Paton factors, so U(N+k|k) is "equivalent" to U(N) via tachyon condensation that annihilates the k D-branes with their antibranes.

    I say "formally" because I don't think that this is really an exact statement. One messes up with the GSO projections etc.

  5. First reaction: This is not good and it smells like trouble but I have to undertand it better.

  6. kashyap vasavadaSep 8, 2014, 4:37:00 PM

    Interesting paper.But is my understanding correct that Vafa may be using exact supersymmetry to cancel anti unitary behavior. What happens if SS is broken? Then you are back to anti unitary behavior. Right?

  7. Lubos , thought you'd be interested...(some scientist on reddit claims global warming is human-caused and that there's no denying it because of a 97% consensus. (peer-reviewed)


    When they assessed their findings, it was out of 11,944 papers that
    mention climate change or global warming. Of that total, there were
    4,014 papers that expressed a position on the cause of climate change.
    97% of the 4,014 papers endorsed the idea of man-made climate change.

    So 7,930 papers were not included in the percentage because those
    papers did not express any position on whether or not climate change is
    man made. Of the total papers examined, 34% endorsed the idea of man made climate change.

    PS: i know it's off topic. sorry about that.

  8. No, I am not interested, and this spam was so brutally off-topic that I instantly blacklisted you. This is a thread about a new paper by Cumrun Vafa, a top theoretical physicist, not a thread meant to promote hardcore cranks who are afraid of "global warming".

  9. It would be interesting to see what Lenny Susskind has to say about this interesting issue ... :-)

  10. Stephen Paul KingSep 9, 2014, 2:19:00 PM

    What?! You are seriously considering unitarity violating theories? How is this possible?

  11. No, I am not. Exactly because I find unitarity so important, I want to know how sharp is the boundary that separates it from the sick, non-unitary theories etc.

    It is plausible that Cumrun really wants to consider non-unitary theories for more reasons than I would. If so, I would add

    1) he may have different opinions and priorities than others (e.g. me) about what principles can be changed

    2) he may consider non-unitary theories because they are still mathematically interesting - in some cases, as interesting as the unitary ones - and the maths behind physical theories is still what he finds most important in stimulating his research

    3) he may be just wrong

  12. Stephen Paul KingSep 9, 2014, 3:02:00 PM

    OK, I was just making sure... I like Cumrun's idea; it is interesting for the reasons that you state. One related question: Is there a violation of the t-duality implied by if the extra fermionic and bosonic "dimensions" exists only at very high energies? This is a complicated question...

  13. LOL, right, very complicated.

    If one gets the fermionic dimensions from K D-brane-antibrane pairs, then the system is unstable. One may probably trade the negative-energy directions for negative-norm directions in some way (I am not sure whether there is a general way to continue a theory in this way because I am no expert in seemingly unphysical theories).

    The instability from brane-antibrane annihilation is an extreme infrared phenomenon, in some sense, so it may become harmless at high energies.

    Too many things to take into account but I ultimately don't understand what's the goal and what is allowed. I prefer to eliminate negative-norm theories entirely.

  14. Stephen Paul KingSep 9, 2014, 5:01:00 PM

    "...eliminate negative-norm theories entirely. ..." If I recall correctly, David Finkelstein (Georgia Tech) has proposed some ideas that seem to allow for local unitarity violations in some interactions involving gravity; but I think that so long as one can re-gain some semblance of unitarity in some large limit, then the math works out.
    My main worry is that we are far away from any physical phenomena that can guide our intuitions as we think about these concepts and often our ideals of "mathematical elegance" can lead us astray.

  15. There exists a D-brane construction that does exactly what Cumrun wants, without any tachyons and with all supersymmetry preserved. These are the "ghost" D-branes by Okuda and Takayanagi (hep-th/0601024).

    The ghost D-brane is defined via the corresponding boundary state, which is simply minus that of an ordinary D-brane (in contrast to the boundary state of the anti-D brane, which only flips the sign of the RR-sector boundary state). They show that a system of N+k ordinary D-branes and k ghost D-branes gives maximally supersymmetric Yang-Mills based on U(N+k|k), just as Cumrun wants. All supersymmetries are preserved.

    So one could hope that the non-unitary AdS/CFT Cumrum is after has as its gravity dual the near-horizon geometry of this Brane/ghost-brane system.

    The only problem with this is that Ghost-branes EXACTLY cancel their D-brane counterpart. The boundary state of a D-brane and a ghost is 0. So there does not seem to be any room for the non-perturbative difference that Cumrun claims got to be there. The N+k with k ghosts system looks indistinguishable from just N D-branes. So either these non-perturbative differences just aren't there in maximally supersymmetric Yang-Mills (despite of what Cumrun says) or the ghost D-branes are more subtle than Okuda and Takayanagi make them sound.

  16. Up-voted only because it made me feel good to intuitively detect that this comment is made by someone so very much in the know and clear about what they are commenting about. Also nice to see when Lubos get something substantial and nicely stimulating out of the 'physics-portion' of his own forum.

  17. Hi Lubos,

    do you have noticed the new media war initiated by Laura Mersini-Houghton stating that black holes not exist ( Correct me if I'm wrong but I think their faulty claim is related to the way the coordinates (they are using) are defined (

    It is so frustrating to see how people like L.M.-H. destroy science...

    Nevertheless, thank you for your great efforts!


  18. Dear Bob, it was discussed yesterday somewhere, wasn't it? ;-)