Preprint typeset in JHEP style- HYPER VERSION Higher Gauge Theory II: 2-Connections (2009)
Abstract: Connections and curvings on gerbes are beginning to play a vital role in differential geometry and theoretical physics — first abelian gerbes, and more recently nonabelian gerbes and the...
Just as gauge theory describes the parallel transport of point particles using connections on bundles, higher gauge theory describes the parallel transport of 1-dimensional objects (e.g. strings)...
Differential twisted String and Fivebrane structures (2009)
Sati, Hisham, Schreiber, Urs, Stasheff, Jim
In the effective background field theory of string theory, the Green-Schwarz anomaly cancellation mechanism plays a key role. Here we reinterpret it and its magnetic dual version in terms of...
Connections on non-abelian Gerbes and their Holonomy (2008)
Schreiber, Urs, Waldorf, Konrad
We introduce transport 2-functors as a new way to describe connections on gerbes with arbitrary strict structure 2-groups. On the one hand, transport 2-functors provide a manifest notion of parallel...
AQFT from n-functorial QFT (2008)
There are essentially two different approaches to the axiomatization of quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and functorial QFT, going back to Atiyah and Segal....
Sati, Hisham, Schreiber, Urs, Stasheff, Jim
We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin...
Preprint typeset in JHEP style- HYPER VERSION Higher Gauge Theory II: 2-Connections (2008)
Abstract: Connections and curvings on gerbes are beginning to play a vital role in differential geometry and theoretical physics — first abelian gerbes, and more recently nonabelian gerbes and the...
Smooth Functors vs. Differential Forms (2008)
Schreiber, Urs, Waldorf, Konrad
We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This way we set up a dictionary between fundamental...
L-infinity algebra connections and applications to String- and Chern-Simons n-transport (2008)
Sati, Hisham, Schreiber, Urs, Stasheff, Jim
We give a generalization of the notion of a Cartan-Ehresmann connection from Lie algebras to L-infinity algebras and use it to study the obstruction theory of lifts through higher String-like...
The inner automorphism 3-group of a strict 2-group (2007)
Roberts, David, Schreiber, Urs
Any group $G$ gives rise to a 2-group of inner automorphisms, $\mathrm{INN}(G)$. It is an old result by Segal that the nerve of this is the universal $G$-bundle. We discuss that, similarly, for every...
Parallel Transport and Functors (2007)
Schreiber, Urs, Waldorf, Konrad
Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize...
Contents joint work, in parts, with (2007)
Urs Schreiber, John Baez, Alissa Crans, Jim Stasheff, Danny Stevenson
From loop space mechanics to nonabelian strings (2005)
Lifting supersymmetric quantum mechanics to loop space yields the superstring. A particle charged under a fiber bundle thereby turns into a string charged under a 2-bundle, or gerbe. This...
Unoriented WZW Models and Holonomy of Bundle Gerbes (2005)
Schreiber, Urs, Schweigert, Christoph, Waldorf, Konrad
The Wess-Zumino term in two-dimensional conformal field theory is best understood as a surface holonomy of a bundle gerbe. We define additional structure for a bundle gerbe that allows to extend the...
Just as gauge theory describes the parallel transport of point particles using connections on bundles, higher gauge theory describes the parallel transport of 1-dimensional objects (e.g. strings)...
From loop space mechanics to nonabelian strings (2005)
Lifting supersymmetric quantum mechanics to loop space yields the superstring. A particle charged under a fiber bundle thereby turns into a string charged under a 2-bundle, or gerbe. This...
From Loop Space Mechanics to Nonabelian Strings (2005)
Lifting supersymmetric quantum mechanics to loop space yields the superstring. A particle charged under a fiber bundle thereby turns into a string charged under a 2-bundle, or gerbe. This...
From Loop Groups to 2-Groups (2005)
Baez, John C., Crans, Alissa S., Stevenson, Danny, Schreiber, Urs
We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where...
Higher Gauge Theory: 2-Connections on 2-Bundles (2004)
Connections and curvings on gerbes are beginning to play a vital role in differential geometry and mathematical physics -- first abelian gerbes, and more recently nonabelian gerbes. These concepts...
Super-Pohlmeyer invariants and boundary states for non-abelian gauge fields (2004)
Aspects of the supersymmetric extension of the Pohlmeyer invariants are studied, and their relation to superstring boundary states for non-abelian gauge fields is discussed. We show that acting with...
Nonabelian 2-forms and loop space connections from SCFT deformations (2004)
It is shown how the deformation of the superconformal generators on the string's worldsheet by a nonabelian super-Wilson line gives rise to a covariant exterior derivative on loop space coming from a...
Discrete Differential Geometry on causal graphs (2004)
Differential calculus on discrete spaces is studied in the manner of non-commutative geometry by representing the differential calculus by an operator algebra on a suitable Krein space. The discrete...
Pohlmeyer invariants are expressible in terms of DDF invariants (2004)
It is shown that the Pohlmeyer invariants of the classical bosonic string are a proper subset of the classical DDF invariants. This makes the quantization of the Pohlmeyer invariants particularly...
DDF and Pohlmeyer invariants of (super)string (2004)
We show how the Pohlmeyer invariants of the bosonic string are expressible in terms of DDF invariants. Quantization of the DDF observables in the usual way yields a consistent quantization of the...
On deformations of 2d SCFTs (2004)
Motivated by the representation of the super Virasoro constraints as generalized Dirac-K{\"a}hler constraints $(d \pm d^\dagger)|\psi> = 0$ on loop space, examples of the most general continuous...
Covariant Hamiltonian evolution in supersymmetric quantum systems (2003)
We develop a general formalism for covariant Hamiltonian evolution of supersymmetric (field) theories by making use of the fact that these can be represented on the exterior bundle over their bosonic...