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I have moved a Properties-section to strict n-category, taken from (infinity,n)-category (where it serves as a preliminary), which collects the statements from section 2 of Barwick&Schommer-Pries (see the refereces there).
Just to be clear, if at wrapped cycle is a multiple of a cycle , would we or wouldn’t we say it wrapped it?
brief category:people-entry for hyperlinking references at AdS3-CFT2 and CS-WZW correspondence
I finally learned about the general abstract story behind the notion of orientation in -cohomology, for an -ring, in terms of trivialization of -associated -bundles – from this lecture by Mike Hopkins
I added some remark about that to orientation in generalized cohomology. Needs more polishing and expansion, but I have to interrupt for the moment.
I thought this should be better developed, and it is. Following the work of Sundholm and Ranta, several people are trying to use dependent type theory to understand natural language. This involves a range of things philosophers care about: anaphora, polysemy, modality, factivity, etc.
It should be interesting to bring this work into contact with the work here on dependent type theory in mathematics and physics. Already I see an overlap in the analysis of modality via a type of worlds, between us here and them in Resolving Modal Anaphora in Dependent Type Semantics on p. 89.
So I’ve started a page dependent type theoretic methods in natural language semantics to list references, and later results.
cross-linked with single trace observables, copied over the relevant paragraphs from there to a new section here: Via single trace observables under AdS/CFT
I gave the entry super vector space some expositional background and a more detailed (pedantic) definition.
starting a small entry here, for ease of hyperlinking. This is to go along with metric Lie algebra
am splitting this off from n-Lie algebra (which should better be renamed to Filippov algebra)
– am being interrupted now – not done yet…
brief category:people-entry for hyperlinking (at Faulkner construction, presently redirecting to M2-brane 3-algebra) this reference:
(I hope I have identified the author’s webpage correctly – if anyone knows, please check)
added some actual text to the category:people entry Roger Penrose
I was looking for a place to record a somewhat more global overview of the notion of locally presentable category, its related notions and its generalizations to higher category theory. But somehow all of the existing entries feel too narrow in focus to accomodate this. So I ended up creating now a new entry titled
Think of this as accomodating material such as one might present in a seminar talk that is meant to bring people with some basic background up to speed with the relevant notions, without going into the wealth of technical lemmas.
I only just started. Will continue in a moment after a short break…
brief category:people-entry for hyperlinking references at M2-brane 3-algebra
starting something – for the moment just to record this reference:
brief category:people-entry for hyperlinking references at configuration space of points and at correlator as differential form on configuration space of points
some minimum, for the moment just so as to bring in infrastructure for stating the Jacobson-Morozov theorem
added these pointers:
An interpretation of the s-rule for D-brane intersections with NS5-branes (Dp-D(p+2) brane intersections and Dp-D(p+4) brane intersections) as a version of the Pauli exclusion principle is discussed in:
Constantin Bachas, Michael Green, Adam Schwimmer, Section 2.3 of: Quantum mechanics and symmetry enhancement in type I’ superstrings, JHEP 9801 :006, 1998 (arXiv:hep-th/9712086)
Constantin Bachas, Michael Green, A Classical Manifestation of the Pauli Exclusion Principle, JHEP 9801 (1998) 015 (arXiv:hep-th/9712187)
to record the result of
finally created intensive and extensive with the topos-theoretic formalization following the concise statement in the introduction of Categories in Continuum Physics
In Robinson arithmetic, I recorded the simplest nonstandard model (with a single nonstandard element ).
The definition and the annotated bibliography are given for Feynman category.
I wonder how useful this could be in related to elucidate the cohomological and motivic quantization via correspondences (Kan extensions in the setup of Feynman categories can help getting the pushforwards, Connes-Kreimer Hopf algebra, Feynman transform (which in some cases gives coefficients in the formal development of the Feynman integal, basically being partition functions, hence connection to graphs).
brief category:people-entry for hyperlinking references at spin chain
added to N=4 D=4 super Yang-Mills theory a section
Properties – Closed expressions for physical observables
with a brief mentioning of integrability of the dilatation operator, MHV amplitudes and planar limit scattering amplitudes.
brief category:people-entry for hyperlinking references at model structure on operads, and Feynman category
brief category:people-entry for hyperlinking references at single trace operator, SYK model and weight systems on chord diagrams in physics
added statement of the universal property (here), first in classical form, then using the sharp modality, and added remark that this should be the categorical semantics of Mike’s remark 3.14 in arXiv:1509.07584
(also replaced the Definition-paragraph with a slightly beautified version)
brief category:people-entry for hyperlinking references at Sachdev-Ye-Kitaev model, Jackiw-Teitelboim gravity but also at weight system and chord diagram
brief category:people-entry for hyperlinking references at Sachdev-Ye-Kitaev model, Jackiw-Teitelboim gravity but also at weight system and chord diagram
brief category:people-entry for hyperlinking references at Sachdev-Ye-Kitaev model, Jackiw-Teitelboim gravity but also at weight system and chord diagram
added the string diagram incarnation of the Lie action property (here), copied over from STU relation.
Will add this also to Jacobi identity
starting something, recording Theorem 6 in
not done yet…
brief category:people-entry for hyperlinking references at black hole information paradox, holographic entanglement entropy and elsewhere