23. Eye on ArXiv: 21 Apr 2008 - SUSY/non-SUSY duality
DmitryAnd so the new week began… Would be fun to finish another paper till Friday (the subject is “IR divergencies in de Sitter space”). In the mean time, let us take a closer look on some papers released to arxives during the previous week.
Although the idea of SUSY/non-SUSY duality may sound a bit contradictory for an unprepared reader :-), there are situations where it seems to exist. The idea of the paper is the following.
Let us consider N=1 SYM with adjoint superfield \Phi. We will choose the superpotential to be
where 
is the field strength superfield.
(In string theory, such superpotentials appear in the situation when D5 branes are wrapped on vanishing cycles of local CY 3-folds and background B-field is added depending holomorphically on one complex coordinate of the 3-fold. This gives 
in the formula above.)
As it turns out, if the function 
is chosen appropriately, there exist vacua in the theory where SUSY is broken. The idea is that 
can be rendered negative for some factors of the gauge group by introducing high-dimensional operators in the Lagrangian. Negative means that gauge theory becomes unstable (w.r.t. Dyson instability) and wants to choose another vacuum. This vacuum turns out to be non-SUSY.
Duality between SUSY and non-SUSY works as follows. We start with effective IR (
) N=1 SYM. The theory depends on couplings t in the formulae above. For each t the authors find two sets of vacua - one is SUSY and one is not. However, only one beween the two is physical for any t (”physical” here means that VEV of chiral field is below 
), so as one changes t, the SUSY solution may leave allowed region of the field space, and SUSY gets (spontaneously) broken.
2. Ruth Gregory, “Braneworld black holes”
Lecture notes on braneworlds and black hole solutions in brane worlds (I strongly recommend them since Ruth is known expert in the field). Let me remind you what is the essence of the problem.
The brane world is 5 dimensional, and matter is localized on the brane. Since we are living on the brane, we expect gravitational potential between two bodies to fall as 
with distance. However, if we construct a 4 dim Schwarzchild like solution (with desirable 
behavior of the grav. potential at large distances), it will actually look like a string in 5 dim Universe. The latter is of course dynamically unstable and the characteristic time scale of the development of this instability is of course much shorter than the evaporation time for 4-dim black hole. Moreove, this instability appears on the purely classical level. If we instead want to construct 5-dim blackhole with spherical event horizon etc., we find that its gravitational potential falls as 
. Please see the lectures to learn what is the present point of view on this issue.
A very critical point of view on Boyle-Steinhardt-Turok PRL paper is introduced. Let me remind you that BST argued that in natural theories of inflation 
is bounded by 0.98 and 
for 
. The latter constraint is very important since one might than expect detection of gravitational waves from the B-mode polarization measurements of CMB (even in current experiments). The authors of the present paper argue that in natural models 
should not be restricted so much. The issue of course is how both groups define the word “natural” itself :-)
The Boyle et al. define this word as follows:
1. The energy density or scalar perturbations generated during inflation have amplitude
on the scales that left the horizon 60 efolds before the end of inflation.
2. The universe undergoes at least 60 efolds of inflation.
3. After inflation, inflaton evolves smoothly to an analytic minimum with 
.
4. If the minimum is metastable, it must be long-lived and 
must be bounded from below.
5. The universe has to be reheated without spoiling large scale homogeneity and isotropy.
Hotchkiss et al. drop the last 4 requirements out. I think, dropping out (3) is reasonable (take old inflation for example, where 
evolves from small to large fields), (5) is not a really strong constraint (coupling of inflaton to matter fields is small in order not to spoil the flatness of the inflaton potential by radiative corrections) and (4) is not very much constraining as well.
4. Ted Jacobson, Aron C. Wall, ” Black Hole Thermodynamics and Lorentz Symmetry”
Lubos Motl was so much faster than me and already has a great discussion of this paper on his blog featuring one of the authors of the paper. The picture emerging :-) is quite clear, and I am not sure I am able to add anything to the discussion. Maybe just this:
1) I think, it is indeed wrong to say that string theory predicts Lorentz violation at high energies. Lorentz invaiance is built into the theory; at high energies gravity is described in terms of dual theory - weakly coupled YM, which is of course Lorentz invariant. It is meaningless to talk in this regime about effective disersion relation for the graviton, because there is simply no such fundamental degree of freedom there (let us be consistent and, say, also discuss what happens with its width as quantum state in high energy regime, in other words, how well the graviton can be described as a particle).
Well, as Lubos Motl immediately pointed out, YM is dual to high curvature limit of the AdS string theory, not high energy limit, strictly speaking. So, that was bullshitting from my side ;-)
2) Suppose that string theory has nothing to do with objective reality (doubt that) and Lorentz violation does take place beyond Planckian scale, as, say, in models of emergent gravity Grigory Volovik likes to talk about (so that effective dispersion relation is
). First trivial thing to notice - if the theory is effectively non-interacting there (i.e., we dealt with asymptotically free theory in the IR, and there is no UV-IR phase transition), then one does not have to care whether 2nd law of thermodynamics holds or not. The form of distribution of particles (species etc.) over energy is frozen, nothing thermalizes.
Second thing - in the opposite case, when interaction is important at higher energies (like in QED), troubles begin. 2nd law of thermodynamics is broken down -> theory there is strongly out of equilbrium (take a look on the name of this blog :-)), thermodynamic unstability develops. It badly messes with everything: even if we say that 2nd law of thermodynamics is effectively valid at low energies and IR degrees of freedom are thermalized quickly, IR dynamics should be influenced by strongly non-equilibrium UV dynamics - phase volume of UV degrees of freedom in Boltzmann integral is large, and they constantly source deviations from thermal equilibrium in the IR.
So, the bottom line, I guess, is that if Lorentz violation may be allowed by a strange flip of Nature, it will be allowed in asymptotically free theories. On the other hand, there are always phase transitions in asymptotically free theories, and IR degrees of freedom are not quite the same as UV ones :-)
The authors calculate the Bayesian posterior probability ratios for three different models that could explain the cold spot: cosmic texture, anomalously large void and Sunyaev-Zeldovich effect caused by a cluster. The texture interpretation is favored, while void and cluster explanations are discarded - temperature decrement produced by them is negligible.
At some point we discussed here the possible explanation of the cold spot as effect caused by a void, so I will outline the statement of the paper regarding void. The radius distribution of voids close to us is known, so the authors take this distribution as prior. It turns out that best fit template corresponds to the radius of void 
MPc and 
. This gives a temperature anisotropy at the level 
, so that the template is completely negligible. Much larger voids do produce a larger temperature decrement but they are strongly penalized by the prior.
6. Diego Chialva, Ulf H. Danielsson, “Chain inflation revisited”
Somehow I forgot to review this paper, although did not to send a trackback to archives :-) Fellow scandinavians somehow forgot to cite us even after I asked them directly by email. I am a friedly guy, though, so will write about their paper.
Diego and Ulf discuss chain inflation as follows from the title. In particular, they determine dynamics of background, construct perturbation theory and introduce a formula for the spectrum of adiabatic perturbations. They also discuss how to embed chain inflation on the landscape - one needs to consider a IIB compactification with fluxes (landscape corresponds to different CY compactifications).
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Also, two new Witten’s papers were released today, and I will have to take a closer look on them to write about them intelligently.
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22. About decoherence in quasi de Sitter space
DmitryMy discussion of disorder on the landscape with Lubos continues (L - Lubos, D - me).
L: So if I understand well, your degree of freedom is really the inflaton phi, and it is one degree of freedom per Hubble patch, with one expectation value and one variation. The value of the inflaton is assumed to directly control the Hubble constant and the size of the patch, according to the normal equations.
D: Yes, I am sure you understood me correctly. What I do is the following: taken a given Hubble patch, I focus only on the dynamics of IR degrees of freedom, that is, the ones with wavelength 
(so that I introduce a coarsegraining). Why can one do this? Physics at superhubble scales may be causally connected during inflation - both particle and event horizons in the de Sitter universe are exponentially larger than 
:
.
After the end of inflation one causally connected patch has the characteristic size , that’s where the notion of Hubble patches actually comes from.
L: So you neglect all higher-frequency modes of the inflaton and other fields which may or may not be a sane truncation.
D: There are two things here: a) I care only about light fields (more or less with 
) and do not care about the others, since they get quickly damped to zero during inflation and b) I do neglect UV modes of the inflaton, because they are in the vacuum state (Bunch-Davies or in-vacuum); particle creation takes place only after a given mode crosses the Hubble scale.
L: Moreover, when you create new causally disconnected bubbles, you probably suddenly increase the number of degrees of freedom of the system, with a new phi per every new patch, don’t you?
D:No, bubbles get causally disconnected only after the end of inflation, so I am happy with that, I don’t introduce anything artificially. It is not actually a new in every patch, it is more like IR fluctuation of the inflaton; expectation values of in each patch are averages over ensemble of patches (that is equivalent to spatial average, to average over randomly distributed quantum phase of ).
L: Such sudden jumps indicate that the original truncation was probably not 100% fair, was it?
D: It is unfare in the same sense as description in terms of kinetic equation (or Fokker-Planck) is unfare compared to full QFT description. So, pretty much fare as long as you understand what you are doing (say, you are not interested in exponentially small corrections to the distribution function ;-))
L: OK, let me accept it. It is some sort of minisuperspace approximation.
D: In fact, it is. You may not know it, but Hartle-Hawking wave function is the 
asymptotics of the probability distribution - solution of the Fokker-Planck equation I was talking about last time.
L: Then, it seems that your answer about the volume factors is a resounding No. If the Hubble radius (and patch) is large, it doesn’t make its value of the cosmological constant more likely. It is still some value of the inflaton, one observable which is the only degree of freedom, right? For the same reason, one doesn’t increase the probability of D3-branes deep inside throats. Isn’t it a prediction that inflation shouldn’t occur then?
D: No, as you can easily see by introducing a model with 
. In the limit 
there will be a distribution of effective cosmological constant values among the Hubble patches given by your favorite Hartle-Hawking wavefunction :-), but inflation will continue to run in each patch.
If one takes chaotic inflationary model, where inflation is actually allowed to end, then the probability for inflation to end is finite (say, one can calculate such things as the average number of efoldings which is not divergent).
L: The “funny thing” you are describing is the traditional freezing of the quantum fluctuations, or something else? Strictly, is it OK to assume that such a process is microscopically a result of decoherence?
D: Yes, it is. One neglects decaying superhubble adiabatic mode compared to the growing one. In practice, decaying part of the mode can be neglected after a couple of efoldings after the given mode leaves the Hubble scale.
L: I am confused about various additional kinds of tools, including superHubble fluctuations.
D: People usually say “superhorizon”, I don’t like it since horizon scale is exponentially larger than during inflation.
L: Those of us who tend to believe complementarity think that these modes don’t really exist because all the information behind the horizon is a scrambled gauge copy of the information inside the horizon (of course, it can be a scrambled copy of some degrees of freedom you omitted), much like in the black hole case. Is that OK to conclude that your picture assumes/implies that complementarity can’t hold?
D: I think this is very much in the spirit of cristianity :-) Just add a God who sits on the horizon (or beyond it) and pulls ropes attached to us through dS/CFT (or AdS/CFT) :-) String theorists are Believers in their hearts :-)
Inflation was not described by de Sitter, it was quasi de Sitter, and the causality structure of quasi de Sitter is so much richer than that of de Sitter. My belief :-) is that it was the reason why dS/CFT was unsucessful.
But if by complimentarity you mean unitarity, even in quasi de Sitter, in the end, unitarity should hold; you just do not have an access to the information stored in deep IR modes. It is the same thing one has in kinetics - there, strictly speaking, thermal equilibrium is never reached, and thre are always exponentially small corrections to the Boltzmann law carrying information about all degrees of freedom. Should be the same in the case of black hole, isn’t it?
L: Sorry if I increased the confusion.
D: No, actually I did, I believe :-) Probably, your readers are bored to death at this point.
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