Higher Gauge, TQFT, quantum gravity thematic convergence

[marcus]

If you follow QG research you will remember that in September 2009 there was a mainly Loop QG school/workshop on Corfu at which several people presented minicourses (John Baez, Carlo Rovelli, Abhay Ashtekar, Vincent Rivasseau, John Barrett...) Each minicourses was a series of 5 onehour lectures. There was also a workshop consisting of individual onehour lectures.

The school was sponsored by the ESF-QG: John Barrett's branch of European Sci. Found that funds Quantum Geometry and Quantum Gravity meetings/research etc.

John Baez' minicourse was an introduction to Higher Gauge Theory. I gather one message here is that HGT fits in and can contribute to QG progress. So we have been kind of waiting for the other shoe to drop. What will the followup be? Where will this go? specifically in the context of 4D geometric quantum gravity?

Baez wrote up his Corfu minicourse in a 60-page paper:
http://arxiv.org/abs/1003.4485
An Invitation to Higher Gauge Theory
John C. Baez, John Huerta
60 pages, based on lectures at the 2nd School and Workshop on Quantum Gravity and Quantum Geometry at the 2009 Corfu Summer Institute
(Submitted on 23 Mar 2010)
"In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincaré 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a 'tangent 2-group', which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an 'inner automorphism 2-group', which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an 'automorphism 2-group', which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a 'string 2-group'. We also touch upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra that governs 11-dimensional supergravity."

The mention of BF theory is significant. This is a type of TQFT (Topological Quantum Field Theory) and the prevailing Spin Foam version of LQG is derived as a constrained BF theory.
So while as mathematics Higher Gauge and TQFT have broad applications to several fields they are specifically applicable to Loop-and-allied QG, and potentially of interest to QG researchers.

One sign of this is the upcoming February 2011 Lisbon school/workshop also sponsored by Barrett's ESF-QG outfit.
https://sites.google.com/site/hgtqgr/programme

The listed speakers are:
Paolo Aschieri (Alessandria)
Benjamin Bahr (Cambridge)
Aristide Baratin (Paris-Orsay)
John Barrett (Nottingham)
Rafael Diaz (Bogotá)
Bianca Dittrich (Potsdam)
Laurent Freidel (Perimeter)
John Huerta (California)
Branislav Jurco (Prague)
Thomas Krajewski (Marseille)
Tim Porter (Bangor)
Hisham Sati (Maryland)
Christopher Schommer-Pries (MIT)
Urs Schreiber (Utrecht)
Jamie Vicary (Oxford)
Konrad Waldorf (Regensburg)
Derek Wise (Erlangen)
Christoph Wockel (Hamburg)

There will be 7 days of school, with minicourses presumably aimed at grad student/entrylevel postdoc. With the last 4 days a workshop with people presenting their research in individual talks, and time for discussion.

 

[AndyW]

Thank you for bringing up the topic of Higher Gauge Theory in the context of 4D geometric quantum gravity. As a scientist working in this field, I can provide some insights into the significance of this theory and its potential applications in quantum gravity research.

As you mentioned, Higher Gauge Theory was introduced by John Baez in his minicourse at the 2009 Corfu Summer Institute. This theory generalizes ordinary gauge theory by incorporating a gauge "2-group" instead of a gauge group. This has important implications for quantum gravity, as it allows for a more comprehensive understanding of parallel transport for particles and strings in terms of 2-connections on 2-bundles.

One of the key applications of Higher Gauge Theory in quantum gravity is its role in the development of spin foam models. These models are derived from constrained BF theory, which is a type of TQFT. By incorporating Higher Gauge Theory, we can potentially improve the accuracy and predictive power of spin foam models, leading to a better understanding of quantum gravity.

Furthermore, Higher Gauge Theory has broad applications in several fields, including string theory and multisymplectic geometry. This makes it a valuable tool for researchers in quantum gravity, as it provides a bridge between different areas of study and allows for a more comprehensive approach to understanding the fundamental nature of spacetime.

The upcoming Lisbon school/workshop, sponsored by Barrett's ESF-QG outfit, is a great opportunity for researchers and students to learn more about Higher Gauge Theory and its applications in quantum gravity. The list of speakers, which includes prominent researchers in the field, indicates the growing interest and potential of this theory in the quantum gravity community.

In conclusion, Higher Gauge Theory is an exciting and promising area of research in 4D geometric quantum gravity. Its potential applications and contributions to the field make it an important topic to follow and explore further. I hope this information has been helpful in addressing your question.