**Chiral gravity conjecture survives a coordinated attack of 11 wrong scientists & Strominger wins**

Chiral gravity is the asymptotically AdS_3 general relativity with the usual Einstein-Hilbert term, a cosmological constant, and a (chiral) gravitational Chern-Simons term. Note that the AdS_3 isometry group is generically SO(2,2) which (locally) decomposes to SL(2,R) x SL(2,R), a group equivalent to the left-moving and right-moving symmetries in a two-dimensional conformal field theory which is the expected dual boundary CFT for all similar gravitational systems.

In January, Wei Li, Wei Song, and Andy Strominger conjectured that something special was going on for a preferred value of the cosmological constant: all the physical excitations become chiral and transform under one of the two SL(2,R) factors only.

More precisely, they showed that the chiral gravity has ghosts or negative-energy modes for generic values of the coefficients so the theory is no good but in the special case, one half of the theory completely decouples, consistency is restored, and the theory becomes chiral. A great example of a typical high-quality Strominger paper about a topic in which he is arguably the #1 leader in the world, or at least in the top 5. (And of course, Wei and Wei are great, too.)

But this conclusion had to run into all kinds of bizarre prejudices held by many people. So it has been criticized at least in 7 papers by at least 11 authors, including S. Carlip, S. Deser, A. Waldron, D.K. Wise; D. Grumiller, N. Johansson; G. Giribet, M. Kleban, M. Porrati; M.i. Park; and R. Jackiw. That's literally the world's top 11 scientists, a scientific consensus organizing a crusade against the paper by Andy, Wei, and Wei. ;-)

Needless to say, Andy Strominger et al. are obviously right. Andy submitted a new simple proof of their conjecture. He shows that all left-moving conformal transformations become trivial (unphysical) at the special point - which everyone should have expected anyway, because c_L = 0 at this point (and only pure gauge states are allowed in a c_L = 0 portion of a healthy theory) - which is why only the right-moving excitations under the conformal group survive. The left-moving excitations can also be seen to carry no energy (because the left-moving stress energy tensor e.g. the Virasoro generators vanish).

There is no known inconsistency of the model at the special value but it has not been strictly proven yet that its physical, right-moving portion is fully OK, too.

**Why all of those guys were wrong**

It is interesting to see why all of those guys have written their mostly wrong papers. Steve Carlip et al. don't expect anything complicated to occur at special points - they pretty much ignore everything one can learn by a more careful analysis of these gravitational models, i.e. from string theory. Most of the authors were not even able to see that "something" special was going on at the special point. That's pretty bad - it's like a person who tries to "disprove" the Riemann Hypothesis but the essence of his proof is that he doesn't even notice that something special is going on on the critical line. ;-)

The authors have also made all kinds of technical errors such as extrapolating solutions from smaller patches (the extrapolations diverge) etc.

But it is even more interesting to look at Matthew Kleban et al. because Matt has been a string theorist. So you might be puzzled why he would reject a manifestly correct paper by Strominger et al. and "kindly" co-sponsor a "translation" of a wrong paper by Carlip et al. into Andy's formalism.

Well, of course, no conspiracy theories about Kleban's treason ;-) are needed. Matt simply didn't understand why the Carlip paper was wrong - namely because the "propagating bulk solutions" that they use as counterexamples are pure gauge - and he chose not to pay much attention to the (very strong) evidence in favor of the conjecture in the original paper. In some sense, Andy didn't realize this particular subtlety either - until his newest paper.

When you look at all the papers from the current perspective, everything looks very clear and makes sense. Because the central charge is zero, every unitary theory has to be empty, so whatever states one could find must be zero-norm, pure gauge states. The appearance of enhanced symmetries at special points is nothing new in quantum gravity or string theory. For instance, at self-dual radii under T-duality, one gets an enhanced gauge symmetry.

But there are cases that are even more similar to what you need here. For example, if you study bosonic string theory in the old covariant quantization, you will have lots of interacting ghosts for wrong spacetime dimensionalities. At D=26, the number of ghosts jumps even more but you can see that all of them actually decouple. They're analogous to the left-moving states that decouple at the chiral point.

The sociological lesson is that most of the people can easily be wrong and most papers written about a subject may be wrong, too. The more fashionable it becomes to write wrong papers of a certain type, the higher the expectation value of the number of wrong papers will be. ;-)

As Ivar Giaever said, the number of scientists is not important. Only those who are correct are important. And moreover, AdS/CFT and string methods work, bitches (and Matt!). ;-)

It seems to be overlooked that there exists

ReplyDeletea first order formalism of 3D gravity al la Cartan, cf.

Mielke, E.W. and A. A. Rinc\'on Maggiolo: ``S-duality in 3D

with torsion", Ann. Phys. (N.Y) {\bf 322}, No. 2, pp. 341-362

(2007), which avoids the 3rd Cotton terms and facilitates the analyzis of propagating modes