## Monday, July 28, 2008 ... //

### A new kind of mirror symmetry

Hep-th papers on Monday

Among the 17 papers that appeared on hep-th today, a majority is about stringy topics. Thank God, things are not getting crazy.

Cvetic and Weigan design a a new "canonical" type of gauge-mediated supersymmetry breaking with an anomalous U(1) and its realization in terms of D-braneworlds in type I string theory. Predictions of superpartner masses, plus minus an order of magnitude, are included.

Joseph and Rajeev identify a (not quite) new classical limit of string theory - at very high densities (string gas cosmology) - and describe its main observables in the Hamiltonian formalism.

McLoughlin and Roiban combined the membrane minirevolution with the Penrose/BMN limit of the AdS4/CFT3 correspondence. Their BMN-like analysis of dimensions of operators in the new N=6 Chern-Simons theory disagrees with some predictions recently made using the Bethe equations.

Bedoya studies the pure spinor formulation of superstring theory at the one-loop level. The one-loop corrections to the nilpotency of Q can be used to calculate Chern-Simons corrections to the Yang-Mills low-energy limit.

Sun discusses the flat directions in supersymmetric theories. They don't exist for generic Kähler potentials in supergravity but when you decouple gravity and simplify the potentials, to end up with global supersymmetry, flat directions often occur. He discusses the stabilized vacua in the middle and the qualitative nature of this interpolation between SUGRA and global SUSY.

Kazama writes down the superstring dynamics in backgrounds with RR-fluxes in the semi-light-cone gauge, clarifying the relationship with the normal light cone gauge (a description we know from the BMN limit).

Aschieri, Ferrara, and Zumino offer an interesting philosophical review of electromagnetic duality or S-duality in four dimensions: the group structure, special features in the supergravity context, and basics of Seiberg-Witten-like theory for the N=2 theories where special Kähler geometry is important.

Klusoň generalizes a procedure to derive the D2-brane action from the M2-brane theory, in the membrane minirevolution, to the more general non-linear case where you don't go to low energies - the Dirac-Born-Infeld action. The first preprint number in his abstract is clearly incorrect. I find the DBI picture of many branes controversial even in the case of D-branes, not only M-branes, but I hope that Josef mostly knows what he is doing.

Kodama, Kokubu, and Sawado study the Einstein-Skyrme model - general relativity with extra scalar fields whose configuration space has a non-trivial homotopy group so that one can "wrap" spacetime configurations on the theory's configuration space. They write down some brane solutions to this theory and discuss its excitations, especially the fermionic ones, with a focus on their masses.

Catelin-Jullien, Faraggi, Kounnas, and Rizos wrote a new paper about their new kind of mirror symmetry for heterotic strings. I believe it's the best paper today and I will talk about it at the end.

Magnen, Rivasseau, and Tanasa look at limits of non-commutative field theories. These theories tend to have a better ultraviolet behavior and may be unexpectedly renormalizable, as a result of the noncommutativity. However, the commutative limit on a "classical geometry" is naively nonrenormalizable. They argue that they have a way to take the limit so that the limit is renormalizable. I have some serious doubts whether it's possible and whether the limit is "more canonical" than other regularizations of the same nonrenormalizable (commutative) theories but I haven't read the whole paper.

Brandhuber, Heslop, and Travaglini discuss a topic that was also covered in several recent papers: the dual superconformal transformations of the N=4 gauge theory, the most famous AdS/CFT example. Very recently, Drummond et al., as well as Berkovits and Maldacena, pointed out a new kind of "fermionic" T-duality in the non-linear sigma model describing the string worldsheet in the AdS5 x S5 background. Once you do this transformation, you end up with an identical model but the original strongly coupled amplitudes can be mapped into a calculation of some specially engineered Wilson loops in the dual theory. The present authors prove the dual superconformal symmetry of the S-matrix of the original (or final) theory.

Billo', Ferro, Frau, Fucito, Lerda, Morales find a lot of D-terms and F-terms in type IIB orbifold flux vacua generated by mostly fractional D-brane instantons.

Rosten links the asymptotic safety of the Wess-Zumino model to the existence of a certain fixed point (with an operator whose anomalous dimension is negative; and with a certain direction keeping some properties of the Kähler potential) using Pohlmeyer's methods and nonrenormalization theorems.

Lalak and Eyton-Williams look at supersymmetry breaking from another angle. They take the Intriligator-Seiberg-Shih model (no, ISS is not the International Space Station in this case), assume a dynamical cancellation of the cosmological constant, generate F-terms of some special type, and conclude that in this gauge-mediated setup, soft scalar masses are about 100 times heavier than gauginos and friends.

Gurau, Magnen, Rivasseau propose their new replacement for both Feynman path integrals as well as Feynman diagrams. In their new framework, only tree Feynman-like diagrams occur. And loops and divergences disappear. ;-) Well, I wouldn't really bet that this paper is correct. Quite on the contrary. Some people are obsessed with the elimination of divergences but they forget that physics is supposed to calculate physical phenomena. I assure similar authors that in the hypothetical case that something like their approach is possible, the first acceptable paper about it will quantitatively re-calculate a well-established quantum (loop) process using the new formalism, rather than just claim, using a lot of Garrett Lisi-like formal nonsense, that a new fantastic gadget exists.

Carlip derives the number of propagating degrees of freedom (one) and dimensions of the boundary CFT operators in topologically massive AdS3/CFT2 by choosing new degrees of freedom in the bulk that simplify the constraint algebra. At least he claims so. ;-)

Spinor-vector duality in heterotic vacua

I chose the paper by Tristan Catelin-Jullien, Alon E. Faraggi, Costas Kounnas, John Rizos to be my daily winner.

They look at the free-fermionic heterotic vacua, favorite models of your humble correspondent from the early 1990s. Most of my computer passwords used to be encoding a short version of the phrase "free-fermionic 4-dimensional heterotic vacua". ;-)

In these models, the 16 "excessive" left-moving bosons on the heterotic worldsheet are fermionized (into 2 fermions per boson, as always), much like the hidden 6 dimensions, leading to a theory with four X_m(sigma,tau) and 32+12 + 8+12=64 fermions in total (counting the light-cone gauge physical degrees of freedom only). A lot of GSO projections (and twisted sectors) acting on subsets of these 64 fermions are postulated.

The resulting spectrum naturally resembles the MSSM/GUT supersymmetric vacua. It is believed that most (or all) of these models describe special points of the moduli spaces of normal heterotic compactifications on Calabi-Yaus, usually orbifold points. But in these particular free-fermionic models, it is very natural for the number of generations to be three.

They have classified large sets of these models and found something that is very reminiscent of mirror symmetry.

If you choose the GUT models with the SO(10) gauge group, you may count the number "V" of the vectorial "10" representations and the number "S" of the spinorial "16" representations of the gauge group. It turns out that for every model with the numbers (V,S), there also exists a model with the numbers (S,V).

These two models are inequivalent at low energies, at least they look so. So it is analogous to type IIA on a Calabi-Yau X and type IIA on a Calabi-Yau Y which is its mirror (the latter is equivalent to type IIB on X): two non-equivalent models. Even in the mirror symmetry case, I don't know a direct physical relationship between "type IIA on X" and "type IIA on Y" except for bookkeeping. So their comments about "topology change" and "different low-energy manifestations of the same high-energy physics" could be more speculative than they think: haven't they forgotten that the two members of their pairs are inequivalent theories?

The models with "S=V" are kind of self-dual (analogous to self-mirror) and they restore some symmetry. In the type II case of mirror symmetry, you would naturally get the same number of vector multiplets and hypermultiplets, expecting some enhanced symmetry (especially supersymmetry), for example if you pick the Calabi-Yau to be a K3 times a two-torus in order to double the number of supercharges.

Analogously, in the present heterotic setup, the S=V case is special. These vacua normally restore the E6 gauge group. Recall that the fundamental representation of E6 is decomposed under the SO(10) subgroup as 16+10+1, giving you the same number of the vectorial and spinorial representations.

At any rate, this is a new pairing between vacua, one that is proven in the new paper. It seems that there are many more similar relationships between string vacua than what we thought. The set of all vacua resembles a brain where every neuron is connected to many other neurons by many synapses.

If you think that a brain is too artificial, then you are probably one of those dumb creationists from Not Even Wrong (such as Roger Schlafly) whom I tried to completely eliminate from this blog. In case I failed in my difficult elimination task, let me boldly inform you that the brain has evolved naturally, too. ;-) The relationships between the vacua in string theory are governed by pure maths that works everywhere, not only in our Universe, and there is consequently nothing artificial or arbitrary about such relationships and nothing artificial or arbitrary about the landscape.

One (or your humble correspondent) could also speculate that these insights are important for the vacuum selection problem. For example, Nature could be naturally preferring vacua that are very close to various symmetries - with small (but nonzero) differences between "S" and "V", among other things.

At any rate, these new relationships should be studied. It should be determined whether the mysterious link between the pairs of vacua has a meaning beyond the perturbative series. The relationship should be interpreted in as many ways as possible and whatever we're doing in the mirror symmetry case should be tried in this case, too.

And that's the memo.