Thursday, May 08, 2008

Hep-th papers on Thursday

Krefl and Walcher derive the - likely - mirror duals of D-branes wrapping cycles of the weighted projective spaces similar to the case of the quintic. Recall that a real slice should be mapped to a holomorphic equation. There's quite impressive math in it. They also write the tensions as holomorphic functions of the moduli space, use the Gromov-Witten expansion, and extract some really cool Ooguri-Vafa invariants (very large integers). All this work can be done at the level of topological string theory.

Costa and Piazza argue that the Unruh effect doesn't exist. ;-) More precisely, the detector won't ever see any radiation, they say. I think that their problem is that they really don't know what it means to accelerate a detector. They write that the results are "model-dependent". Sorry but when you put jets beneath a detector and turn them on, something very specific will happen and a good physicist should be able to calculate it. When she does so, she will see that radiation is observed because a Bogoliubov transformation must be used to switch the two Hamiltonians as well as the the corresponding ground state and creation/annihilation operators.

Of course, when you forget about this transformation, you will get a wrong, radiation-free answer. A 2008 paper about basics of the Unruh effect that doesn't contain any "Bogoliubov transformation" is simply bizarre. And I think it is wrong.

Kitazawa studies the fate of light open-string modes in braneworld toy models. The real task is to calculate loop corrections to their squared masses - with a focus on its sign - after supersymmetry is broken. The calculation should be relevant for various type IIA braneworlds. The author would like to construct realistic braneworld models with radiative electroweak symmetry breaking.

van Baalen, Kreimer, Uminsky, Yeats investigate the running coupling in QED and similar theories beyond perturbative expansions. The paper is written as a math paper about differential equations, with lemmas and proofs. I don't exactly understand what the very task is supposed to mean because QED is inconsistent beyond perturbation theory. Or is it not? Nevertheless, they have an interesting answer to an otherwise meaningless question about the non-perturbative existence of the Landau poles (and of a separatrix). The answer involves the asymptotic growth of the skeleton graphs, encoded in a function P(x). Because they can't really decide what the function is, I guess that the answer remains incomplete.

Houri, Oota, Yasui classify all "integrable" manifolds of a certain kind. These manifolds should have a rank-2 closed conformal Killing-Yano tensor. It is equivalent to a tower of Killing-Yano and Killing tensors. Their existence allows one to solve the geodesic equations and to completely separate the Hamilton-Jacobi, Klein-Gordon, and Dirac equations on these manifolds. Because the Kerr-NUT-deSitter metric (a rotating black hole in a space with a positive cosmological constant based on the NUT spaces) is an example, the resulting geometries may be viewed as their multi-dimensional generalizations. I suppose that they have some solutions beyond those of Chen-Lü-Pope but I can't tell you what they are. Read it.

Loginov logs in and extends the ADHM method to eight dimensions, to construct exact solitonic solutions of the heterotic string's low-energy equations. A generalized self-duality on the eight-dimensional space, presenting it as the direct sum of two quaternionic spaces, is needed. But the formulae are otherwise ratios of polynomials analogous to the normal ADHM setup.

Rafiei, Jalalzadeh, Tabrizi look at kinks in 1+1-dimensional scalar theories. The action has the kinetic and potential terms. The well-known potentials, sine-Gordon and quartic, are generalized to more general "shape-invariant" potentials although I am not quite sure what they are. The one-loop corrections to the kink masses involve generalized zeta functions.

Evans and Threlfall deform the AdS/CFT by a dilaton flow in the bulk. The boundary dual of the deformation is an SO(6)-invariant mass. At high temperatures, this leads to the AdS-Schwarzschild solution and a Hawking-Page transition. An extra transition restoring the chiral symmetry is found in the mix.

Huang looks for the AdS/CFT bulk description of glueballs found in gauge theories deformed both by non-commutativity as well as a dipole parameter. He writes down a specific SUGRA solution, a ratio of polynomials. The glueballs have a discrete spectrum. The spacing is governed by the inverse dipole length (and a velocity factor) in the supersymmetric case.

Ross wrote a note about NLO (next-to-leading order) of the BFKL (Balitskii, Fadin, Kuraev, Lipatov) kernel, an object in QCD. And because I don't really know what it is, I won't comment on this paper.

Ruffino and Savelli try to clarify the relationship between K-theory frameworks to classify D-brane charges. The first statement one must swallow is that there are two K-theory algorithms to do so. One based on the Atiyah-Hirzebruch spectral sequence classifies charges conserved in time - that's probably what most of us imagine - while the other classifies whole trajectories.

At the rational level, both of them are equivalent (and also coincide with cohomology) but at the integer level, they are different. There is still a relationship between them but I didn't understand what the relationship is supposed to be. Quite generally, I don't understand the exact problem they are trying to solve. Because of all this confusion about the right answer, my personal conclusion is that none of the known well-defined simple mathematical objects based on K-theory describes the actual stringy physics exactly which, in my opinion, should mean that K-theory shouldn't be presented as a tool that is necessary for string theory. A full physical analysis is still needed.

Gomis, Milanesi, Russo continue in the membrane minirevolution. They can construct infinitely many new 3-algebras, one for each Lie group, but only if they allow the metric on the 3-algebra space to be indefinite. In fact, it has one time-like direction: a Minkowski signature. One can imagine that we add 1+1 dimensions to the original Lie algebra and define the 4-structure constants as f^{+abc}=C^{abc} for a light-like direction "+" while others vanish: C^{abc} are the Lie algebra structure constants.

In Yang-Mills theory, this fancy Minkowski feature would instantly violate unitarity, because of the kinetic term. However, the Bagger-Lambert-Gustavsson theory is really a Chern-Simons theory so the violation is not obvious although they can't yet prove that the physical Hilbert space is actually positive definite. ;-) At any rate, it is pretty fascinating. Their candidate theory is promising since it reduces to the U(N) gauge theory after Higgsing (plus one decoupled ghost). There should be a way to kill the ghost direction from the scratch, by finding a new, unexpected gauge symmetry (playing the same de-ghosting role as the conformal symmetry on a worldsheet).

Knapp and Scheidegger study a similar problem as the first paper in this list, namely the mirror symmetry for D-branes on Calabi-Yau manifolds. Various BPS invariants for low-genus open worldsheet instantons are calculated.

Cicoli, Conlon, Quevedo claim to have found a geometric condition that is necessary and sufficient for moduli stabilization at large volumes. Their answer is that if the Euler character is negative and if there exists at least one blow-up mode resolving point-like singularities, string loops are able to stabilize the volume at a large value. K3 fibrations are their favorite example.

Finally, let me end up with a sociological observation that I find absolutely stunning. Among the 14 pretty interesting hep-th papers above, there is only one (1) that includes authors affiliated with the U.S. institutions (van Baalen et al.). We are talking about a discipline that has been literally led by the U.S. for decades. I think that one of the key explanations is the lethal impact of Mr Woit, Mr Smolin, and similar breathtakingly dishonest far-left anti-scientific subhuman activist garbage. The American physics was just incapable to destroy these disgraceful, cheap jerks and liars, so these jerks are now free to destroy the American physics. This is where appeasement with scum may lead. An example where a death penalty is too little, too late.


  1. About arXiv:0805.1009 ("Comparing two different K-theoretical classifications of D-branes"), we'd like to point out that there has been a misunderstanding. With this article, we don't want to motivate the use of K-theory to classify D-brane charges, since this has been done by Witten, Minasian and Moore for the first approach, and by Maldacena, Moore and Seiberg for the second. Since both approaches, which we summarized, are considered good in literature (by very important authors), there is the problem of relating two good classifications of the same thing. The conclusion we reached could be not so clear at a first look, since there is a very technical part concerning in particular spectral sequences, but, after a preliminary study of it, the statement is quite clear: AHSS gives an equivalence class of K-theory elements, while Gysin map (at a fixed instant) gives a representative element of such a class.

    The authors

  2. Thank you very much for your explanations. So is it OK to say that the K-theory as a set is identical in both approaches - it's just that the Gysin map contains more information than the AHSS, by picking the element from each class?

    Is this additional information included in the Gysin map physical or does it depend on some conventions or arbitrary details of the procedure?

    If the answer to the question above is that the sets are different in the two approaches, which of them is correct?

  3. Yes, K-theory is a unique set, the same for both approaches. The additional information provided by Gysin map is physical, since it concernes the gauge bundle and the gravitational coupling of the D-brane. The problem is that Gysin map, when restricted to a fixed instant, is not a charge conserved in time (it can be different at another instant). Instead, AHSS, which is applied at a fixed instant, deletes anomalous cycles and gives a charge conserved in time (the equivalence class reached).

    Thus, the two approaches are complementary: AHSS detects possible anomalies and instabilities, and, for "healthy" branes, the Gysin map gives the trajectory information and the coupling to the action.

    One can ask if we can improve AHSS approach, adding information about the couplings. We don't know the exact answer. Maybe, it is related to the equivalence classes at higher dimensions than the codimension of the brane (the ending point of AHSS is the graded group associated to a certain filtration of K-theory).

    Fabio Ferrari Ruffino

    Raffaele Savelli