network profile
| bio | website | ncatlab.org/nlab/show/… |
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| location | ||
| age | 92 | |
| visits | member for | 1 year, 7 months |
| seen | May 10 at 11:52 | |
| stats | profile views | 115 |
I am a postdoc in mathematics, but have my degree in theoretical physics. My work is about mathematical structures motivated from quantum field theory and string theory. For more see my personal web on the nLab.
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Apr 19 |
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fitting free QFTs into the Haag-Kastler algebraic formulation I don't do science by counting citations, but if forced to prove a point here by pointing to the authority of citations I might point to Longo-Witten's arxiv.org/abs/1004.0616 which uses AQFT to study issues that remained with Witten's old "Some computations in background independent Open-String Field Theory". |
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Apr 19 |
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fitting free QFTs into the Haag-Kastler algebraic formulation Exception of what? In fact, the application of AQFT to 2d CFT has been most succesful, see ncatlab.org/nlab/show/conformal+net for references. I like to think of this as being a bit ironic: many AQFT textbooks start out being motivated by understanding 4d YM and disliking string theory, but then most hard and important results are obtained in classification of 2d CFT, and string theory has probably profited more from this effort than 4d QFT has. |
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Feb 23 |
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Discussions of the axioms of AQFT I have added the page number. Anything else that is "wrong"? What do you find messy about the links? |
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Feb 18 |
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Poisson structure on moduli space of CFTs Squark is right, I think. Phase space is precisely the space of classical solutions. (See the references by Witten at ncatlab.org/nlab/show/phase+space) Only in nice situations are these given by a global initial value problem that allows identification with a cotangent bundle. Non-nice situations include gauge theories and theories of gravity, and we know that the space of CFTs contains both. |
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Feb 17 |
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Poisson structure on moduli space of CFTs Hi Squark: an action and a BV bracket, yes. That's what one needs for a phase space in this description. So it may be a different approach than what you thought of, but I think it goes exactly in the direction of answering your question. Of course this is just an incomplete story, yes. I am not sure if this has been followed up since. |
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Feb 8 |
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String-theoretic significance of extended CFT ... If one of the two is trivial, then this is a boundary condition for the other one and makes it an open/close theory. |
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Feb 8 |
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String-theoretic significance of extended CFT Some good observations on a possible systematic formalization of the relation between extended QFT and open-closed QFT/ QFT with defects are towards the end of the slides "Topological Defects and Classifying Local Topological Field Theories in Low Dimensions" ncatlab.org/nlab/files/SchommerPriesDefects.pdf by Chris Schommer-Pries. There from slide 65 on it is shown that specifiying a ("almost natural") transformation between two 2d extended TQFTs (regarded as 2-functors on extended cobordisms) amounts to giving the data of a defect junction between the two QFTs. ... |
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Feb 6 |
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String-theoretic significance of extended CFT Examples of modular invariants that do not correspond to a full CFT are listed on page 3 of arxiv.org/abs/hep-th/0204148. |
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Feb 6 |
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String-theoretic significance of extended CFT Hi Squark, try out this crisp summary (3 pages) of FRS: mth.kcl.ac.uk/staff/i_runkel/PDF/ost.pdf I suppose this addresses several of the points raised here, keeping in mind that the results that they refer to are obtained with a state-sum construction as for extedned TFT but internal to the given modular tensor category of VOA representations. |
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Feb 6 |
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String-theoretic significance of extended CFT Hi Squark, yes, in these extended pictures the closed sector typically arises from the open sector, which is more fundamental. You will see this amplified in the article by Kong that I mentioned. It is worked out in much detail in work by Fuchs-Runkel-Schweigert (FRS). See notably their article "Uniqueness of open/closed rational CFT with given algebra of open states" projecteuclid.org/… |
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Oct 22 |
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Geometric Langlands as a partially defined topological field theory No, I mean the "2-space" of states, the A-oo algebra of string states assigned to the point. This is not a fully dualizable object for the A- and B-model. |
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Oct 22 |
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Super Lie-infinity algebra of closed superstring field theory? There is indeed no distinction, and that's what I wanted to implicitly emphasize a little, with an eye towards the BLG "3-algebra" excitement ncatlab.org/nlab/show/BLG+model#3AlgebraStructure. |
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Oct 21 |
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Is there a background independent closed string field theory? Sure, but you asked "is there background independent CSFT?". The closest to manifest background invariance in CSFT that I am aware of is Sen, Zwiebach "Background Independent Algebraic Structures in Closed String Field Theory" (arXiv:hep-th/9408053) |
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Oct 21 |
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Paper listing known Seiberg-dual pairs of N=1 gauge theories Thanks, done. Hm, that might need more discussion. |
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Oct 18 |
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Sympletic structure of General Relativity Ron, the first line of the OP's question asks for the symplectic structure of the GR phase space and whether it has a Liouville form. My answer, after a lead-in paragraph on what the phase space actually is, discusses both of these structures on phase space. |
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Oct 17 |
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Is ghost-number a physical reality/observable? Okay, I have written out in more detail and with more explanations the things that I have said here so far at ncatlab.org/nlab/show/BRST+complex . If you have a look and then let me know which questions you have next, I'll try to to answer these and explain more. |
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Oct 17 |
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Which QFTs were rigorously constructed? By the way, just for the record: while maybe it does not count as a "full construction", there has recently been quite some work on how to turn the usual tools of perturbative QFT into rigorous constructions of "perturbative AQFT nets". Some references are here ncatlab.org/nlab/show/perturbation%20theory#ReferencesInAQFT |
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Oct 17 |
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Which QFTs were rigorously constructed? Yes, for nontrivial topology. That's what I mean by "for all genera". Kong's construction also deals with that case, though less explicitly, I think. |
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Oct 17 |
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Is ghost-number a physical reality/observable? ...field configurations. But, you know, I see that there is no way of having all this decently discussed in these puny comment boxes here. We'll have to move this discussion elsewhere. Let me see. I'll write out a longer reply elsewhere and then point you to it. |
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Oct 17 |
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Is ghost-number a physical reality/observable? ...the given complex to the complex R[-n], which is the complex concentrated on the ground field in degree n and with trivial differential. Now, if this cochain complex is also equipped with a product that respects the differential, then it is called a dg-algebra, and the notion of cohomology still applies. The BRST complex is an example of such a dg-algebra. Being an algebra, we can think of it as being the "algebra of functions on some space" and define that space thereby. For the case of the BRST complex this space is the infinitesimal version of a Lie groupoid, the Lie groupoid of... |
