Monday, July 30, 2012

The counterpart of AdS5 duality in TGD framework

The generalization of AdS5 duality of N=4 SYMs to TGD framework is highly suggestive and states that string world sheets and partonic 2-surfaces play a dual role in the construction of M-matrices. In the following I give an argument providing a "proof" of this duality and also demonstrating that for singular string world sheets and partonic 2-surfaces perturbative description of generalized Feynman diagrams is especially simple since string effectively reduces to point like particles.

Some terminology first.

  1. Let us agree that string world sheets and partonic 2-surfaces refer to 2-surfaces in the slicing of space-time region defined by Hermitian structure or Hamilton-Jacobi structure.
  2. Let us also agree that singular string world sheets and partonic 2-surfaces are surfaces at which the effective metric defined by the anticommutators of the modified gamma matrices degenerates to effectively 2-D one.
  3. Braid strands at wormhole throats in turn would be loci at which the induced metric of the string world sheet transforms from Euclidian to Minkowskian as the signature of induced metric changes from Euclidian to Minkowskian.
AdS5 duality suggest that string world sheets are in the same role as string world sheets of 10-D space connecting branes in AdS5 duality for N=4 SYM. What is important is that there should exist a duality meaning two manners to calculate the amplitudes. What the duality could mean now?
  1. Also in TGD framework the first manner would be string model like description using string world sheets. The second one would be a generalization of conformal QFT at light-like 3-surfaces (allowing generalized conformal symmetry) defining the lines of generalized Feynman diagram. The correlation functions to be calculated would have points at the intersections of partonic 2-surfaces and string world sheets and would represent braid ends.

  2. General Coordinate Invariance (GCI) implies that physics should be codable by 3-surfaces. Light-like 3-surfaces define 3-surfaces of this kind and same applies to space-like 3-surfaces. There are also preferred 3-surfaces of this kind. The orbits of 2-D wormhole throats at which 4-metric degenerates to 3-dimensional one define preferred light-like 3-surfaces. Also the space-like 3-surfaces at the ends of space-time surface at light-like boundaries of causal diamonds (CDs) define preferred space-like 3-surfaces. Both light-like and space-like 3-surfaces should code for the same physics and therefore their intersections defining partonic 2-surfaces plus the 4-D tangent space data at them should be enough to code for physics. This is strong form of GCI implying effective 2-dimensionality. As a special case one obtains singular string world sheets at which the effective metric reduces to 2-dimensional and singular partonic 2-surfaces defining the wormhole throats. For these 2-surfaces situation could be especially simple mathematically.

  3. The guess inspired by strong GCI is that string world sheet -partonic 2-surface duality holds true. The functional integrals over the deformations of 2 kinds of 2-surfaces should give the same result so tthat functional integration over either kinds of 2-surfaces should be enough. Note that the members of a given pair in the slicing intersect at discrete set of points and these points define braid ends carrying fermion number. Discretization and braid picture follow automatically.

  4. Scattering amplitudes in the twistorial approach could be thus calculated by using any pair in the slicing - or only either member of the pair if the analog of AdS5 duality holds true as argued. The possibility to choose any pair in the slicing means general coordinate invariance as a symmetry of the Kähler metric of WCW and of the entire theory suggested already early: Kähler functions for difference choices in the slicing would differ by a real part of holomorphic function and give rise to same Kähler metric of "world of classical worlds" (WCW). For a general pair one obtains functional integral over deformations of space-time surface inducing deformations of 2-surfaces with only other kind 2-surface contributing to amplitude. This means the analog of stringy QFT: Minkowskian or Euclidian string theory depending on choice.

  5. For singular string world sheets and partonic 2-surfaces an enormous simplification results. The propagators for fermions and correlation functions for deformations reduce to 1-D instead of being 2-D: the propagation takes place only along the light-like lines at which the string world sheets with Euclidian signature (inside CP2 like regions) change to those with Minkowskian signature of induced metric. The local reduction of space-time dimension would be very real for particles moving along sub-manifolds at which higher dimensional space-time has reduced metric dimenson: they cannot get out from lower-D sub-manifold. This is like ending down to 1-D black hole interior and one would obtain the analog of ordinary Feynman diagrammatics. This kind of Feynman diagrammatics involving only braid strands is what I have indeed ended up earlier so that it seems that I can trust good intuition combined with a sloppy mathematics sometimes works;-).

    These singular lines represent orbits of point like particles carrying fermion number at the orbits of wormhole throats. Furthermore, in this representation the expansions coming from string world sheets and partonic 2-surfaces are identical automatically. This follows from the fact that only the light-like lines connecting points common to singular string world sheets and singular partonic 2-surfaces appear as propagator lines!

  6. The TGD analog of AdS5 duality of N=4 SUSYs would be trivially true as an identity in this special case, and the good guess is that it is true also generally. One could indeed use integral over either string world sheets or partonic 2-sheets to deduce the amplitudes.
What is important to notice that singularities of Feynman diagrams crucial for the Grassmannian approach of Nima and others would correspond at space-time level 2-D singularities of the effective metric defined by the modified gamma matrices defined as contractions of canonical momentum currents for Kähler action with ordinary gamma matrices of the imbedding space and therefore directly reflecting classical dynamics.

For background see the new chapter The recent vision about preferred extremals and solutions of the modified Dirac equation of "Quantum TGD as Infinite-Dimensional Geometry" or the article with the same title.


Ulla said...
Much of the exciting action is space is confined to thin boundaries. The Universe is filled with plasma, a charged gas consisting of ions and electrons. Thin sheets with currents separate large plasma regions in space. Scientists at the Swedish Institute of Space Physics (IRF) have now finally measured the fundamental properties of one of the waves mixing and accelerating plasmas within these sheets. Majorana particles
Sign reversal of the boson-boson interaction potential for the planar Bose-Fermi mixtures under synthetic magnetic field

Ulla said...
physicists have begun to ask whether there might be some other interesting complexities in the second law, particularly when they take into account the quantum nature of particles.

How might quantum mechanics play a role? One possibility is related to the weird phenomenon of entanglement in which two particles become so deeply linked that they share the same existence, even when they are separated by the width of the universe. When two particles are entangled, a measurement on one gives you information about both particles.

matti Pitkanen said...

It would be nice second law were finally submitted under critical discussions. I have tried to talk about these aspect - also possible new physics involved with second law - during last years. Typical view about second law - say that of Lubos - forgets all assumptions needed to derive Botzmann's equations.

This same pattern of forgetting basic assumptions repeats itself like fractal everywhere in theoretical physics nowadays.

Quantum measurement theory does not even exist in any serious sense in recent day quantum theory so that its problems contain certainly the roots of new physics and even of theory of consciousness. It is completely isolated from the theoretical physics which enjoys funding: to get the feeling about what establishments wants you to thin just read the postings of Lubos.

SUSY is routinely taken the standard SUSY although it involves a lot of un-necessary assumptions- including super-space formalism, which dictates the theory to a high degree. Despite that fatal blows of LHC nothing changes. Again: read Lubos: he is conservative as he repeatedly says and therefore his blog has become a graveyard of dead ideas;-).

The assumptions behind GUT and Higgs paradigms are very strong and several of basic predictions such as proton decay are not observed and one ends up with fine tuning. This does not seem to worry anyone enjoying salary as a theoretical physicist. Did I already mention the blog of Lubos;-)? He goes even further and regards the newly discovered spinless particle as synonymous with Higgs!

For some reason - probably the inability to admit that we might have gone astray for several decades and the fear to lose funding - colleagues enjoying monthly salary stubbornly continue in the chosen direction.

Ulla said...

Stuart Kauffman has an idea of 'order for free', which maybe can be translated into this view. He wants to have a fourth law of thermodynamics. I have also seen other views of the second law that would explain biology, and surprisingly also Bolzmann, like two branches on the same tree. This means that the conservative view on the second law is wrong.

Ulla said...
Sheehan researched the chemical reactions of molecules when they are surrounded by a perfect vacuum and acted upon by the Casimir effect, a phenomenon discovered 60 years ago that explains why surfaces separated by a microscopic vacuum gap can be slightly attracted to one another.

Using a simple thermodynamic argument, Sheehan shows that in principle the Casimir effect can be used to finely tune and drive chemical reactions on one surface across a perfect vacuum simply by moving a nearby surface with respect to it. In other words, reactions can be mechanically altered without the exchange of any real material particles or energy.

oil and gas professional, says his linkedln page.

Ulla said...

A video about the need to update the second law, by Sheehan!

Matti Pitkanen said...

There are many reasons for updating second law in TGD Universe.

a) Macroscopic quantum coherence in long time scales implies that Bolzmann's equations fail below the time scale of coherence (hierarchy of Planck constants and scales of coherence).

b) The possibility of negentropic entanglement also requires updating (p-adics especially relevant for biology). The new element is the possibility to generate genuine negentropy locally. The conservative view about second law is that in sufficiently long scales second law wins but alternative can be considered.

c) The recent TGD based view about the arrow of time requires also updating.

*At the level of 8-D imbedding space arrow of time alternates: quantum jumps are alternetely state function reductions to the "upper" and "lower" boundary of causal diamond (intersection of future and past directed lightcones essentially).

*At the level of space-time the observed arrow stays constant as is clear by using entropy as time coordinate. This corresponds to subjective arrow of time.

Observer getting information only about her own space-time sheet is a Flatlander not able to perceive the change of the imbedding space arrow in state function reductions assignable to the ends of CD. For instance, entropy is natural time variable and increases monotonically as long as second law in generalized sense holds true.

By observing what happens at other CDs flatlander can discover that the imbedding space arrow varies. We have done this: Itialian physicists Fantappie realized already at fourties that in living matter one must speak also about syntropy- the identification is as entropy for reversed arrow of imbedding space time. Biological self-assembly processes could be a good example: actually they represent entropic process but in direction direction of imbedding space time associated our CD.

This view looks rather radical re-interpretation but it is extremely economic: one actually gets rid of the U-process since quantum jump is just state function reduction to either boundary of CD defining at the same time U-matrix as matrix relating zero energy states with opposite arrows of imbedding space time.

Matti Pitkanen said...

By the way: I made a little breakthrough in understanding of how pion like state can behave in very Higgsy manner in the decays to electroweak bosons but at the same time produce anomalously high gamma pair production.

There are simple killer tests. I hope that SUSY Higgses inspire similar tests- in particular search for the charged partners of Higgs candidate.

Also a direct connection to the leptopion hypothesis emerges: the model for the leptopion product generalizes practically as such and vacuum expectation of pion like field replaces Higgs expectation.

Strong feeling that the situation is now settled and I can wait for the experimental verification of M_89 hadron physics with a calm mind;-).

See the new posting at .

Ulla said...

Congratulations :-) Good with a calm mind :) Maybe you get boring? GUT2012

Ulla said...
Ed Witten. The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.

Bosons:fermions or continuous :descreate systems?

Matti Pitkanen said...

To Ulla:

I added my response as a posting: