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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 here.


Aug
27
comment Why does string theory have such a huge landscape?
...akin to the Dirac charge quantization condition which makes anything finite in this game at all. Moreover, the higher these integral periods are, the more they contribute to some potential energy. Some other constraints say that this energy cannot be too big. So as a rule of thumb on says that one has a choice between 10 different values for each such flux field on each cycle. Similarly, as a rule of thumb, one says that a generic Calabi-Yau has 500 nontrivial cylces, give or take a few hundred. The conclusion of this thumb-counting is that the number of choices for the flux fields is...
Aug
27
comment Why does string theory have such a huge landscape?
No, that number 10^500 which has become so famous in public discussion plays no specific role. It is just a generic example of the following counting: 1. IF one assumes that 10 spacetime is compactified on a Calabi-Yau (which one used to be interested in (only) because this makes the effective 4d thory N=1 supersymmetric) and 2. IF one considers type II "flux vacua", then the highr form fields of string theory (the higher electromagnetic fields, if you wish) are quantized/constrained to have integral periods over the cycles of the compact Calabi-Yau. It is this quantization condition, akin...
Aug
27
answered Why does string theory have such a huge landscape?
Aug
27
comment What is Mathematical formulation of entropic Gravitational force?
I thought the article was the low-level explanation...
Aug
26
comment In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?
Yeah, I would even say not only that it does not matter in practice, but that this is exactly what is secretly happening in practice anyway. All is just as it should be. (Except that it can get really confusing to talk about universes in this sense in a physics forum! ;-)
Aug
26
comment In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?
@Francois: good point, but just for completeness notice this: while plain dependent type theory does not have the syntactic analog of a subobject classifier, as you say, in the version of intensional type theory now called homotopy type theory (ncatlab.org/nlab/show/homotopy+type+theory) such a "type of propositions" (ncatlab.org/nlab/show/type+of+propositions) does exist, even a "type of types" does (ncatlab.org/nlab/show/type+of+types), which makes intensional dependent type theory with the "univalence axiom" a language for (higher) toposes, indeed.
Aug
26
comment In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?
...which makes them fit nicely in the broader context of algebraic and higher/derived geometry, which is all about modelling spaces by ringed toposes (ncatlab.org/nlab/show/structured+(infinity,1)-topos). In Nuiten's discussion of quantum field theory by Bohr toposes it is crucial that the causal locality axiom is encoded as a descent condition of such ringed toposes. So for that application to QFT I tend to prefer them, but for basic statements one can just as well use the other model.
Aug
26
comment In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?
@Mozibur, the difference is that Isham-Doering look at contravariant functors on commutative subalgebras with inclusions between them, while Heunen-Landsman-Spitters look at covariant functors. The basic statements about observables work in both formulations. Sander Wolters has a a bit of discussion of the relation between the two in "A Comparison of Two Topos-Theoretic Approaches to Quantum Theory" arxiv.org/abs/1010.2031 . In the perspective of Heunen-Landsman-Spitters the Bohr toposes are naturally ringed toposes (ncatlab.org/nlab/show/ringed+topos) which makes them...
Aug
26
revised What is Mathematical formulation of Holographic principle?
added 29 characters in body
Aug
26
answered What is Mathematical formulation of Holographic principle?
Aug
26
revised In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?
edited body
Aug
26
answered Has anyone ever tried to formulate physics based on computer science or information processing?
Aug
26
revised In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?
edited body
Aug
26
answered In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?
Aug
24
answered Strings and their masses
Aug
22
comment experimental bounds on microcausality violation
@Ben, that's of course a good point. Somehow I was hoping for something fancier, but I guess you must be right.
Aug
22
asked experimental bounds on microcausality violation
Aug
20
answered The Chern-Simons/WZW correspondence
Aug
13
revised Obtaining supergravity from gauging global supersymmetry
fixed grammar and fine-tuned somebody else's edit that highlights that the last citation is a self-citation
Aug
10
comment Obtaining supergravity from gauging global supersymmetry
But apart from their role as higher gauge groups under which higher branes are charged, higher Lie groups also appear as "higher orbispace" target spaces on which higher branes may propagate. This is the second role mentioned in the above reply. For instance the supergravity Lie 3-algebra is also the target "higher super-orbispace" which is such that a sigma-model map into is a combination of a map to spacetime and a 2-form on the worldvolume. This way it serves as a higher geometric target space that renders the 5-brane a genuine, albeit "higher" sigma model.