## Monday, May 29, 2006

### Hep-th papers on Monday

Oriol Pujolas looks at the DGP model. If you don't know, the DGP model is a popular model among the phenomenologists in which you have a five-dimensional gravity with a 3-brane in it, and the action contains both the bulk 5-dimensional Einstein-Hilbert term ("integral R.sqrt(-g)") as well as an additional 4-dimensional Einstein-Hilbert term that is stuck on the 3-brane. The latter term is unlikely to appear in string theory, I think. At distances shorter than a crossover scale - usually assumed to be the Hubble scale without a good reason - gravity looks 4-dimensional. At longer distances, the bulk term starts to dominate and gravity is 5-dimensional. Pujolas studies quantum fluctuations in this model: the author computes some Green's functions, and a one-loop effective potential arising from the quantum fluctuations.

J.C. Bueno Sanchez and K. Dimopoulos study a new kind of inflation based on a rolling scalar field - a quintessence. Although the picture is string-inspired, it does not seem that they are talking about a specific well-defined background in string theory. Their description of the "trapped quintessential inflation" has many stages and it reads like a novel. The first stage of their inflation starts in a steep potential, hypothetically generated by non-perturbative effects in string theory. Then you reach an ESP - enhanced symmetry point - where you produce a lot of light particles. They argue that this leads to a period of inflation which I don't quite understand; is a strong particle production compatible with inflation? At any rate, the scalar fields eventually leave the ESP point and go into another steep region, which gives you reheating. Then the scalars freeze because of cosmological friction. It is fixed for a long time until the present, when it starts to behave as a quintessence and roll towards vanishing vacuum energy. A pretty complicated picture combining many pieces that are popular. It seems that we don't have enough data to check each wheel and gear of the construction (and similar constructions). As far as I am concerned, the "supply" of various detailed proposals about inflation exceeds the "demand" - as expressed by the observational data and the need to reconcile interesting ideas - by orders of magnitude.

Rudnei Ramos and Marcus Pinto investigate phase transitions in certain non-relativistic field theories with a lot of scalar fields. They argue that they have proved a no-go theorem: the models of this kind, describing things like hard spheres, can exhibit neither inverse symmetry breaking (which means that a symmetry is broken at high temperatures instead of the usual low temperatures) nor symmetry non-restoration (which describes a situation in which the symmetry is not restored even at very high temperatures). Finally they focus on a specific model that includes a Bose-Einstein condensate in the phase diagram. There is no reentrant phase (an intermediate phase with a partial symmetry breaking) in this model, but they argue that other models might have it.

Canoura, Edelstein, and Ramallo investigate the AdS/CFT correspondence with Sasaki-Einstein manifolds and additional D-branes. As you can see, that combines two concepts. One of them is the class of Sasaki-Einstein manifolds L^{a,b,c}. These manifolds have topology of "S2 x S3". The metric is rather complicated but for a choice of three positive integers "a,b,c", you can follow Cvetic, Lu, Page, Pope, as well as Martelli and Sparks, and construct a manifold whose topology is "S2 x S3" such that the cone constructed above this base is a Calabi-Yau three-fold. The second ingredient of the paper are additional D-branes (referred to as "D-brane probes") added into the bulk. They add bulk open string degrees of freedom on the AdS side, and flavors on the CFT side. The paper may be viewed as Witten's construction of di-baryonic operators implemented in the case of the complicated Sasaki-Einstein manifolds replacing Witten's simple five-sphere. Impressive math.

Alfonso Ramallo has another paper about a similar topic. He also adds D-branes in the AdS bulk. In fact, he wants to consider intersecting D-branes. Such D-branes generate new fields - flavors or "quarks" - in the dual gauge theory. Such "quarks" can form bound states - mesons. Ramallo claims to be able to compute the spectrum of such mesons in a rather general case where the D-branes can have rather general dimensions. He uses the quenched approximations - the D-branes are treated as probes.

Anacleto, Nascimento, and Petrov study non-commutative field theories, especially their UV behavior. The particular theory they consider has a real scalar field with a quartic potential and a Dirac field coupled by a Yukawa term. They choose the "coherent state approach". It seems that it means that this allows them to make the propagators suppressed by "exp(-theta.p^2/2)" relatively to the propagators in the "ordinary" approach that are the same as in the commutative counterpart of the theory (because the kinetic term is the same). Using the Schwinger parameterization, they end up with an integral for the one-loop effective potential that clearly converges for nonzero values of the noncommutativity "theta": at high values of "t", the Schwinger parameter, the integrand is exponentially suppressed. Also, there is a cancellation whenever the quartic coupling and the Yukawa coupling are related to each other in a way that resembles the supersymmetric relation (even though in their particular theory, there is just one real boson field, and no SUSY). At any rate, I think that the nontrivial divergence structure only occurs at the two-loop level where you can see the UV-IR mixing and similar things, but they don't get that far, so I doubt that the experts in noncommutative field theory will be thrilled. In fact, I am confused how they can get different formulae at one-loop than the formulae that have been calculated many times in the past.

Raphael Bousso tries to define a better probabilistic distribution for the landscape than anyone else, and he is approaching this problem in a typically Boussian i.e. holographic way. Recently we discussed Vilenkin's approach to the question of the probabilities on the landscape. They end up with a pile of ambiguous and contradictory mess, and Raphael is rightfully dissatisfied with these anthropic results. His first principle is that only one causal diamond should be looked at when you calculate the probabilities. This sounds correct to me because regions of spacetime behind a particular diamond could be complementary to the diamond itself: they may be described by the same degrees of freedom and you should not double-count them.

His ultimate definition of the probability distribution is relatively simple. Consider the set of stable and unstable vacua that you want to include into your landscape game. Some of them are "terminal" (usually denoted "Z" in Bousso's paper and having a negative vacuum energy) - and they don't decay. Others are unstable (labeled "A,B" etc.) and they do decay. Raphael looks at genealogy trees of these vacua. Each mother vacuum can decay to the daughter vacua, and Raphael only uses the "branching ratios" i.e. the probabilities that "A" decays to "B" or "Z". I hope that he knows how to calculate these dimensionless branching ratios from the instanton actions and vacuum energies but I don't see the rule in the paper. Instead, he focuses on the ultimate probability distribution for the vacua calculated from the branching ratios for the decay. It is virtually identical to Google's PageRank algorithm, as long as you replace (weighted) hyperlinks between web pages by decay channels between vacua, and Raphael can obtain finite results for the probabilities (PageRank) of different vacua whenever there exists at least one available terminal vacuum. If it exists, small trees dominate Raphael's ensemble. Raphael does not say which vacua of string theory ultimately end up with the highest PageRank, but someone else could have an answer. I agree that Raphael's calculation is more justified than the random ad hoc anthropic prescriptions that various people want to apply to the eternal inflation, but I think that much more work is needed to extract useful information from Raphael's semi-anthropic approach even if it is correct.