tag:blogger.com,1999:blog-10614348.post443159251335721978..comments2023-03-18T02:32:07.872-07:00Comments on TGD diary: About the structure of Yangian algebra and 4-D generalization of conformal QFTMatti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-10614348.post-82945638156999946552011-09-01T23:28:44.255-07:002011-09-01T23:28:44.255-07:00Continuation of previous response….
Still a coupl...Continuation of previous response….<br /><br />Still a couple of observations relating to M-theory-TGD connection.<br /><br /><br />G_2 symmetry as automorphisms of octonions is also essential for quaternionic spinor structure and also for the <a href="http://tgd.wippiespace.com/public_html/articles/prefextremals.pdf" rel="nofollow">proposed solution ansatz</a>. I think that G_2 plays key role in M-theory compactifications as symmetries of 7-D compact space.<br /><br />Finally a comment concerning 5-branes whose orbits are 6-branes. <a href="http://tgd.wippiespace.com/public_html/tgdquant/tgdquant.html#Yangian" rel="nofollow">Twistorial approach</a> suggests an alternative view to see TGD. Space-time surfaces would in this picture correspond to 6-D surfaces which are sphere bundles in CP_3xCP_3. The first CP_3 would correspond to twistors. Second would relate to CP_2. Does this mean some connection with F-theory. <br /><br />The essential difference to M-theory is that in TGD space-time regions can have both Minkowskian and Euclidian signatures and light-like 3-surfaces representing particles correspond to 3-surfaces at which the signature changes so that also induced 4-D metric tensor is degenerate, not only 3-D metric tensor.matpitka@luukku.comhttp://tgd.wippiespace.com/public_html/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-10437356176482135052011-09-01T23:22:37.944-07:002011-09-01T23:22:37.944-07:00Continuation to previous response…..
The dimens...Continuation to previous response…..<br /><br /><br />The dimension 10 pop up often in TGD inspired numerology. Also the role of octonions in TGD suggests a connection of some kind. Octonionic projective space has SO(1,9) as its symmetries as John Baez has shown (SO(1,9) is analogous to Mobius SO(1,3) acting in complex plane). He believes that there is a deep connection between string models and octonions. <br /><br /><br />In TGD space-time surfaces are conjectured to be quaternionic surfaces of 8-D imbedding space with octonionic structure in tangent space (for gamma matrices in octonionic representation). Quite recently I realized that the old dream about much more concrete meaning for quaternionicity could be equivalent with this picture. <br /><br />The question is whether preferred extremals of Kaehler action could be expressed as octonion real-analytic in preferred octonionic coordinates for Euclidian version of M^4xCP_2. One would map M^4xCP_2 tp E^4xCP_2 by Wick rotation, perform the octonion real-analytic map f, identify space-time sheet as the quaternionic space-time surface defined by the condition of the "imaginary" part of f(o), and return back by Wick rotation.<br /><br />This map from Minkowskian strings to Euclidian strings is made routinely in string theory. The octonionic Wicki rotation could be also understood in terms of complexification of octonions.<br /><br />For details see <a href="http://tgd.wippiespace.com/public_html/articles/prefextremals.pdf" rel="nofollow">this</a>.<br /><br />To be continued…..matpitka@luukku.comhttp://tgd.wippiespace.com/public_html/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-67000762995022149032011-09-01T23:16:42.118-07:002011-09-01T23:16:42.118-07:00You are right. Concerning standard model quantum n...You are right. Concerning standard model quantum numbers M^4 and CP_2 are necessary and these appear among other this in AdS5xCP2xT2. Torus however gives additional quantum numbers. <br /><br />One can of course argue that the imbedding space in TGD is something quite different from target space in M-theory. These target spaces can emerge as effective imbedding spaces from free field representations of Kac-Moody algebras. <br /><br />As a fact, in TGD this kind of representations seem to emerge in TGD as correlate for finite measurement resolution. The number of braid strands of braid effectively replacing partonic 2 surface defines the dimension of Cartan algebra for Lie algebra defining Kac-Moody algebra. This dimension in turn would characterize the number of transversal degrees of freedom for target space and would have nothing to do with real imbedding space dimension. One might argue that the dimension 10, 11,12 of superstrings, M-theory, F-theory,…is this kind of effective dimension and the interpretation has totally misled theoreticians to spend rest of their life in the muds of M-theory landscape;-). <br /><br />At least all simply laced Lie groups can appear as dynamical gauge/Kac Moody groups with confinement characterizing measurement resolution described in terms of inclusion of hyper-finite factors and I have the impression that free field representations are much more general: the articles of Ed Frenkel about this are however too technical for me and I am also lazy. <br /><br />One might say that finite measurement resolution makes it possible to simulate theories with at least simply laced Lie groups. TGD Universe would be analog of Turing machine. See the end of <a href="http://tgd.wippiespace.com/public_html/pdfpool/Yangian.pdf" rel="nofollow">this</a>.<br /><br />To be continued…..matpitka@luukku.comhttp://tgd.wippiespace.com/public_html/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-76487589866812319212011-09-01T20:55:23.941-07:002011-09-01T20:55:23.941-07:00It might even be that the 3-surfaces of TGD could ...It might even be that the 3-surfaces of TGD could be related to M5-branes of M-theory on this background, compactified on the T^2.Mitchellhttps://www.blogger.com/profile/10768655514143252049noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-46603022964293090012011-09-01T20:53:04.069-07:002011-09-01T20:53:04.069-07:00I just found something surprising: Type IIB string...I just found <a href="http://arxiv.org/abs/hep-th/9803061" rel="nofollow">something surprising</a>: Type IIB string theory on AdS5 x S5, which is the Maldacena dual of N=4 Yang-Mills, is itself T-dual to Type IIA string theory on AdS5 x CP2 x S1, or equivalently M-theory on AdS5 x CP2 x T2. I was always curious about the possibility that TGD closely resembles some M-theory background, and this last background space seems very close to M4 x CP2: you just have M4 becoming AdS5, with four-dimensional energy scale turning into the AdS dimension in the familiar way, and then an extra factor of T2.Mitchellhttps://www.blogger.com/profile/10768655514143252049noreply@blogger.com