Thursday, September 10, 2009

Review of the membrane minirevolution and other hep-th papers

Today, there are twelve new papers primarily labeled as hep-th papers. The first one, and one that may attract the highest number of readers, is a review of the membrane minirevolution by Klebanov and Torri. However, I will mention the remaining eleven preprints, too.

Membrane uprising: a review

The membrane minirevolution was discussed on this blog as a minirevolution long before most people noticed that there was a minirevolution going on.

Important papers by Bagger + Lambert and by Gustavsson (BLG) introduced a new, unusual Chern-Simons-like theory with 16 supercharges in 2+1 dimensions. It was argued that it had to describe two coincident M2-branes. It used to be thought that the CFT theories dual to M-theory on "AdS4 x S7/G" had no Lagrangian description except that BLG found one.

Their theory - originally described in terms of 3-algebras and other unnecessarily novel concepts - was really nice, nontrivial and symmetric only in the case of two coincident M2-branes. Many people tried to generalize it. They eventually realized that the obvious generalizations for many M2-branes either predicted ghosts or they were equivalent to Super Yang-Mills theories or otherwise uninteresting.

The right generalization was eventually found by Aharony, Bergman, Jafferis, and Maldacena (ABJM). Unlike the BLG theory, it only had 12 supercharges. Their theory is an "U(N) x U(N)" Chern-Simons theory at level "k". It describes M2-branes stuck on "M^3 x R^8 / Z_k" whose near-horizon geometry is clearly "AdS_4 x S^7 / Z_k": the "Z_k" group diagonally rotates all four complex coordinates in the transverse "R^8".

The supersymmetry is enhanced from the manifest 12 supercharges to 16 supercharges for the "k=1" or "k=2" cases. Klebanov and Torri show that new monopole operators - impurities or defects - produce the additional 12 currents that combine with the 16 currents of "U(1) x SU(4)" into 28 currents of "SO(8)", a group needed to show the presence of those 4 additional, a priori non-manifest supercharges.

By the way, it's time for an M5-brane minirevolution, too. ;-)


Instantons are topologically nontrivial solution in Euclidean spacetime that are localized both in space and (especially) time: they appear at one instant of time which gives them the name.

What are the calorons? Well, they must have something to do with heat. Indeed, one has a periodic Euclidean "thermal" time here. So they're instanton with a periodic time. It is also easy to see that multi-calorons are calorons whose instanton charge exceeds one; it is equal to two in their case.

Nakamula and Sakaguchi discuss the Nahm equations (ADHM construction of the monopoles) in this context. If you don't know, the Nahm equations are "dM1/dt = [M2,M3]" and its cyclic permutations. The Jacobi elliptic functions appear in their exact solution. Some interesting insights are found but it's too special and mysterious a subject for me to pretend that I have been waiting for these results. ;-)

Glowing rotating string

Matsuo considers bosonic string theory. He takes a highly exciting, rotating fundamental string and calculates its thermal emission. There's some similarity with the Kerr black holes' thermal behavior but if the author conjectures a full duality rather than an order-of-magnitude similarity (like in Horowitz-Polchinski), then I must say that I would be skeptical about such a duality.

Non-commutative theories averaged over theta

Sami Saxell published his or her thesis. It reviews some basic facts about non-commutative field theories, Seiberg-Witten insights about them, and other well-known things. When it comes to new ideas, the thesis focuses on the averaging over many values of the non-commutative parameters, meant to obtain a Lorentz-invariant theory.

Such an averaging creates problems for unitarity (it's like Coleman's calculations of the baby universes) and it seems that the author is well aware of these and similar lethal problems of theories constructed in this way but he or she still needed to write a fine enough thesis about something. ;-)

Black hole instabilities in Klebanov-Strassler

Butcher and Saffin discuss the bulk side of the Klebanov-Strassler theory. They add a perturbation with some momentum and look what's going on. The size of the solution is stable but some perturbations are claimed to create black holes that affect the throat's tip. The authors think that some applications of the Klebanov-Strassler geometry have therefore been physically unacceptable.

Non-relativistic cold atoms from massive type IIA

Singh takes the Romans theory, i.e. a massive version of type IIA string theory in 10 dimensions, and constructs some "AdS4 x S6" solutions where the "AdS4" is Galilean, however. It is claimed that such an ugly AdS-like background is directly relevant for the AdS/AtomicPhysics duality. The other side, with cold atoms, is also ugly which is why the proposed duality has just passed one consistency check. ;-)

AdS/AtomicPhysics on domain walls

Wapler studies 2+1D domain walls - coming from a kind of D5-brane in this case - in a 3+1D spacetime occupied by the N=4 gauge theory via AdS/CFT. The domain wall is given a finite magnetic field, mass, and charge density. Various cyclotron, plasmon, and hydrodynamic phenomena are being calculated in this setup. That's surely a lot of fun for condensed-matter and atomic physical minds.

A bizarre "renormalization scheme"

Grange, Mathiot, Mutet, and Werner argue that a particular unusual approach to "renormalization" is very efficient for dynamics in the light-cone gauge. The "Taylor-Lagrange renormalization scheme" is based on some ad hoc looking restriction of the allowed test functions and they claim to eliminate the need for the "cancellation of infinities".

Although they promote the method as being very efficient at very high orders, they only truncate their reasoning to an approximation with at most two particles. At any rate, I think that this whole way of thinking is misguided. The choices made to restrict the allowed test functions are effectively equivalent to the introduction of the same uncertainties one gets in ordinary "renormalization schemes".

Moreover, I don't think that they use the term "renormalization scheme" in the standard way. Historically, the dominance of obscure papers from the 1960s and 1970s among their references doesn't look too promising.

Differential equations for Calabi-Yau three-folds

Santillan works on some equations written down by Fayyazuddin.

The differential equations relevant for Calabi-Yau three-fold metrics are reduced to a mathematical problem where objects only depend on two real variables. Some equations are even claimed to become linear and the author concludes that they may even be solved in terms of elliptic functions or something like that.

Of course, such analytically solvable metrics have to be non-compact but their subclasses are nicely non-singular and geodesically complete.

Fully SUSic solutions in N=2 SUGRA

Hristov, Looyestijn, and Vandoren look for configurations that preserve all eight supercharges in N=2, d=4 supergravity. Their diversity is obtained by different "electric gaugings" in the hypermultiplet and vector multiplet sectors. They link these SUGRA solutions to type IIB flux compactifications studied by Jeremy Michelson in 1996 and his followers.

AdS/QCD: scalar glueballs from QN modest

Miranda et al. use AdS/QCD to say something about the scalar glueballs. The answers are obtained from Green's functions of an AdS5 black hole with a dilaton soft-wall background. Quasiparticle peaks at low temperatures are important features; their data are equivalent to the data about the black hole quasinormal modes.

An updated review of superstring phenomenology

Massimo Bianchi wrote a somewhat sketchy introductory review of flux compactifications and various stringy braneworlds, as a celebration of the 25th anniversary of the Green-Schwarz mechanism. It is a useful review for those who want to be reminded about the basic classes of the conceivable phenomenological scenarios - qualitatively different types of compactifications - in string theory. When it comes to the experiments, Bianchi seems to be intrigued by signatures of anomalous U(1) groups.

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