Workshop on Higher Gauge Theory and Higher Quantization
Heriot-Watt University, Edinburgh - June 26/27 2014


The hopefully final schedule is listed below.

Thursday, 26. June

10.00Martin WolfSelf-dual higher gauge theory
11.15Sam PalmerN=(1,0) SUSY in six dimensions, self-dual strings and higher instantons
14.00Jeffrey Morton2-Group symmetries on moduli spaces in higher gauge theory
15.15David RobertsExplicit string bundles
16.30Discussion SessionHigher Bundles

Friday, 27. June

10.00Thomas StroblNew methods in gauge theories
11.15Urs SchreiberMotivation for higher geometric quantum theory
14.00Urs SchreiberHigher geometric quantum theory
15.15Patricia RitterLie 2-algebra models
16.30Branislav JurcoOperads, homotopy algebras and strings


Branislav Jurco

Operads, homotopy algebras and strings Notes

We verify that certain algebras appearing in string field theory are algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are explained from the operadic point of view.

Jeffrey Morton

2-Group symmetries on moduli spaces in higher gauge theory Slides | Paper

This talk will describe, in the context of higher gauge theory, a higher-algebraic analog of the relationship between global and local symmetry, described in terms of group actions, and local symmetry, described in terms of groupoids. In gauge theory, the groupoid of connections, constructed locally as a category of transport functors, is equivalent to a transformation groupoid associated to the global action of the full group of all gauge transformations on the full moduli space of connections. We will see that an analogous result for higher gauge theory based on a 2-group is rather more subtle. Since transformation groupoids for 2-group actions are double groupoids, we introduce a double groupoid of transport functors which allows us to distinguish two types of gauge transformations. This gives an analogous equivalence of the global and local view of the symmetries of the moduli spaces of 2-connections.

Sam Palmer

N=(1,0) SUSY in six dimensions, self-dual strings and higher instantons Slides | Paper 1 | Paper 2

Recently much progress has been made constructing models with N=(1,0) SUSY in six dimensions as a stepping stone towards the elusive N=(2,0) theory. These models have a large overlap with higher gauge theory. In particular, the algebraic structures can be recast in terms of strong homotopy Lie algebras, also known as L_\infty algebras. This limited amount of supersymmetry should still be enough to consider M2-M5 brane intersections (self-dual strings). We will look at some explicit solutions for these, as well as what we call 'higher instantons'. These considerations will lead to a plethora of open questions.

Patricia Ritter

Lie 2-algebra models Paper

Inspired by the matrix models proposed as non-perturbative string theories, we propose a generalisation of the IKKT action based on the categorification of the underlying Lie algebra structure to semistrict 2-algebras. After a brief review of the features of the traditional model, we will set up the necessary structures that will allow us to write a 0-dimensional 2-algebra model, containing the IKKT model and some proposed M-brane models as special cases. Since 2-plectic manifolds (i.e. the categorification of symplectic ones) come endowed with a semistrict 2-algebra structure, it is then natural to ask whether a quantisation thereof satisfies the equations we get from varying our categorified action. Indeed we will find this to be the case, for the 2-plectic versions of the various symplectic spaces that solve the IKKT model. We consider this, among other things, a strong indication that this type of categorification is a step in the right direction towards non-perturbative M-theory models.

David Roberts

Explicit string bundles Notes

While higher bundles are of clear relevance to higher gauge theory, examples other than abelian bundle gerbes are hard to come across. One would in particular like to see 2-bundles where the structure 2-group is the string 2-group associated to a compact simple simply-connected Lie group. This talk will outline a method to construct many examples over homogeneous spaces. We shall also consider one example in detail, giving explicit formulas for the crossed-module-valued Cech cocycle arising from a local trivialisation.

Urs Schreiber

Motivation for higher geometric quantum theory Material on ncatlab

This introductory talk reviews motivation for a theory of higher geometric quantization. The theory, as far as it already exists, may be thought of as the generalization of geometric quantization to local covariant de Donder-Weyl field theory. But a special case deserves particular attention: the geometric quantization of 4k+3 dimensional Chern-Simons theories and their holographic self-dual boundary theories in dimensions 4k+2. I review central aspects of this as explained by Witten and Hopkins-Singer.

Urs Schreiber

Higher geometric quantum theory

This talk discusses aspects of a systematic formulation of higher geometric prequantum theory. First I show how traditional geometric quantum theory lifts from symplectic phase spaces to n-plectic moduli stacks of higher gauge fields. Then I consider specifically the special case of 4k+3-dimensional Chern-Simons theory and discuss how its higher phase space stacks refine the traditional intermediate Jacobians whose geometric quantization yields the theta-characteristics of self-dual higher gauge theories. (This is joint work with D. Fiorenza and in parts with C. Rogers).

Thomas Strobl

New methods in gauge theories Paper 1 | Paper 2 | Paper 3 | Paper 4 | Paper 5

Conventional gauge theories (in the setting of a trivial bundle structure) can be explained as lifting a rigid finite-dimensional symmetry group G to a gauge symmetry Maps(spacetime,G) on a functional on an extended field space. We comment on various ways to transcend this conventional understanding: leading to gauge symmetries with Lie n-groupoids playing the role of G or functional defined by higher geometrical structures which turn out to be universal with respect to the above mentioned G-governed ones.

Martin Wolf

Self-dual higher gauge theory Slides | Paper 1 | Paper 2 | Paper 3 | Paper 4

I will review recent work on the formulation of self-dual higher gauge theory in six dimensions using twistor theory.