A contribution for a book on mathematical aspects of QFT, on extended (“multi-tiered”) prequantum Chern-Simons theory formulated in terms of higher geometry.
Below are various recent job offers in maths that colleagues are asking me to circulate. One in Liverpool on motives. One in Prague, on geometry and algebra. One in Erlangen, on higher categories and TQFT. One in Adelaide, on…
A web-based journal for publications in mathematics and physics for topics that are usefully viewed from the point of view of higher category theory and homotopy theory.
In another thread Tom Leinster would like to learn what a sigma-model in quantum field theory is. Here I want to explain this in a way that will make perfect sense to Tom, and hopefully even intrigue him. To…
This week at MPI Bonn is (or has been) taking place a conference in honor of Alan Carey’s 60th birthday. on “noncommutative geometry and index theory, statistical models, geometric issues in quantum field theory. Hamiltonian anomalies and bundle n-gerbes”….
The nCafé is currently affected by a bug that prevents comments to be posted. Here is a link to discussion on the nForum to alleviate this problem for the moment.
This week in our Journal Club on [[geometric ∞\infty-function theory]] Bruce Bartlett talks about section 3 of “Integral Transforms”: perfect stacks. So far we had Week 1: Alex Hoffnung on Introduction Week 2, myself on Preliminaries See here for…
Preliminaries for the discussion of geometric infinity-function theory: higher categories, higher sheaves, higher algebra, higher traces and what it all means.
A place to discuss and learn about the work by Ben-Zvi/Francis/Nadler on geometric infinity-function theory and its application in infinity-quantum field theory.
On local nets constructed from transport 2-functors and examples relating to lattice models, Hopf spin chains, asymptotic inclusion of subfactors. And some remarks on the relation between conformal nets and vertex operator algebras.
A quick review of Landsman’s result on strict deformation quantization of Poisson manifolds dual to Lie algebroids: the quantum algebra is nothing but the groupoid algebra of the Lie groupoid integrating the Lie algebroid.
Some basics and some aspects of geometric quantization. With an emphasis on the geometric quantization of duals of Lie algebras and duals of Lie algebroids.
An article which discusses lifts through the 7-fold connected cover of the structure group of the tangent bundle in the context of electric-magnetic duality in string theory.
A discussion of differential nonabelian cocycles classifying higher bundles with connection in the context of the general theory of descent and cohomology with coefficients in infnity-category valued presheaves as formalized by Ross Street.
Generalized charges are very well understood using generalized differential cohomology. Here I relate that to the nonabelian differential cohomology of n-bundles with connection.
Bruce Bartlett talks about some aspects of the program of systematically understanding the quantization of Sigma-models in terms of sending parallel transport n-functors to the cobordism representations which encode the quantum field theory of the n-particles charged under them.
On how to interpret the geometric construction by Brylinksi and McLaughlin of Cech cocycles classified by Pontrjagin classes as obstructions to lifts of G-bundles to String(G)-2-bundles.
Associated L-infinity structures are obtained from Lie action infinity-algebroids, leading to a concept of sections and covariant derivatives in this context.
On how integration and transgression of differential forms is realized in terms of inner homs applied to transport n-functors and their corresponding Lie oo-algebraic connection data.
On the notion of topos-theoretic quantum state objects, the proposed definition by Isham and Doering and a proposal for a simplified modification for the class of theories given by charged n-particle sigma-models.
On the general idea of transgression of n-connections and on the underlying machinery of generalized smooth spaces and their differential graded-commutative algebras of differential forms.
On the notion of concordance of 2-bundles and, more generally, on a notion of omega-anafunctor and a possible closed structure on the category of omega-categories with omega-anafunctors between them.
Some elements of BV formalism, or rather of the Koszul-Tate-Chevalley-Eilenberg resolution, in a simple setup with ideosyncratic remarks on higher vector spaces.
On the general ideal of integrating Lie n-algebras in the context of rational homotopy theory, and about Sullivan’s old article on this issue in particular.
Nils Baas on higher order structures, Enrico Vitale on weak cokernels and a speculation on weak Lie n-algebras triggered by discussion with Pavol Severa.
What makes the Kontsevich-Cattaneo-Felder theorem tick? How can it be that an n-dimensional quantum field theory is encoded in an (n+1)-dimensional one?
A review of elements of the Batalin-Vilkovisky formalism, with an eye towards my claim that this describes configuration spaces which are Lie n-algebroids.
Hendryk Pfeiffer asked me to forward the following question to the Café. Dear nn-category people, I have a question about tensor categories on which I would appreciate comments and references. As probably several people are interested in this, I…
The concept of an “Adinkra” - a graph used to describe representations of N-extended d=1 supersymmetry algebras - remarkably resembles some categorical structures which appear in the context of supersymmetry.
Passing from locally to globally refined extended QFTs by means of the adjointness property of the Gray tensor product of the n-particle with the timeline.
We propose and study a notion of a tangent (n+1)-bundle to an arbitrary n-category. Despite its simplicity, this notion turns out to be useful, as we shall indicate.
How transformations of extended d-dimensional quantum field theories are related to (d-1)-dimensional quantum field theories. How this is known either as twisting or as, in fact, holography.
A menagerie of examples of Lie n-algebras and of connections taking values in these, including the String 2-connection and the Chern-Simons 3-connection.
A list of some papers involved in the historical development of the idea of expressing bundles with connection in terms of their parallel transport around loops.
A question by Bruce Bartlett about categories of algebras, algebras as categories and the possible implications for non-commutative algebraic geometry.