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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.


Apr
19
comment 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".
Apr
19
comment 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.
Apr
19
answered fitting free QFTs into the Haag-Kastler algebraic formulation
Feb
23
comment 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?
Feb
22
answered Discussions of the axioms of AQFT
Feb
18
comment 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.
Feb
17
comment 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.
Feb
16
answered Poisson structure on moduli space of CFTs
Feb
10
answered Spatial and polarizing beam splitters in a graphical calculus
Feb
8
comment 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.
Feb
8
comment 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. ...
Feb
6
comment 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.
Feb
6
comment 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.
Feb
6
comment 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/…
Feb
6
answered String-theoretic significance of extended CFT
Oct
22
comment 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.
Oct
22
comment 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.
Oct
21
comment 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)
Oct
21
answered Is there a background independent closed string field theory?
Oct
21
comment Paper listing known Seiberg-dual pairs of N=1 gauge theories
Thanks, done. Hm, that might need more discussion.