Defects in two dimensional field theories
Objective
Topic(s)
FP7PEOPLE2009IEF  Marie Curie Action: "IntraEuropean Fellowships for Career Development"
Funding Scheme
MCIEF  IntraEuropean Fellowships (IEF)
Coordinator
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Address
Rue Michel Ange 3
75794 Paris
France
Activity type
Research Organisations
EU Contribution
€ 157 945,60
Administrative Contact
Liliane Flabbee (Ms.)
Project information
D2DFT
Grant agreement ID: 254456
Status
Closed project

Start date
1 September 2010

End date
31 August 2012
Funded under:
FP7PEOPLE

Overall budget:
€ 157 945,60

EU contribution
€ 157 945,60
Mathematical experiments test quantum gravity theories
INDUSTRIAL TECHNOLOGIES
The Standard Model of particle physics is a broadly accepted theory of the particles and forces that make up the Universe. However, it has a few acknowledged gaps, one of the most important being that it does not include a satisfactory description of gravity. This is one of the most pressing open issues in particle physics today. The graviton, the 'gravity' particle that is predicted to exist, may one day be found. For now, existing experimental techniques are forced to rely on mathematical descriptions of graviton, giving rise to gravitational anomalies. As an example for gravitational anomaly, we can consider the difference between actual planet movement measurements and the predicted movement from a model. Quantum gravity is thus a concept of particle physics, and quantum field theory is a branch of mathematics that helps to describe and explain it. There are an infinite number of quantum field theories but the right systems of equations providing selfconsistency need to be applied. In other words, the right equations and the conditions that can solve these equations need to be determined. Scientists initiated the EUfunded project 'Defects in two dimensional field theories' (D2DFT) to investigate specific consistency conditions not well characterised to date — that is, the cancellation of global gravitational anomalies in the field theory description at low energies. Two field theories related to supergravity — string theory and Mtheory, give rise to gravitational anomalies. The anomaly formula has been known for the one since the 1980s but has remained out of reach for the second (the socalled selfdual field theory). Researchers successfully determined the formula for the global gravitational anomaly of selfdual field theories. This has important implications in the field of mathematics and particle physics, leading to an eventual description of quantum gravity. Work encompassed a broad mix of mathematical subfields and scientists are currently exploring the cancellation of global gravitational anomalies to evaluate concepts related to quantum gravity. Gravity may be the glue that holds the Universe together. Scientists are one step closer to defining it on a quantum level — physically and mathematically, thanks to work carried out by the D2DFT project.
Project information
D2DFT
Grant agreement ID: 254456
Status
Closed project

Start date
1 September 2010

End date
31 August 2012
Funded under:
FP7PEOPLE

Overall budget:
€ 157 945,60

EU contribution
€ 157 945,60
Discover other articles in the same domain of application
Final Report Summary  D2DFT (Defects in two dimensional field theories)
This means that we have to build it relying only on its selfconsistency. That such a task should be possible at all is far from obvious. After all, the 'Standard Model' is just one member, singled out by experiments, of a potentially infinite number of quantum field theories. The main surprise which came out of string theory is that consistency arguments single out a unique and still largely unknown structure, Mtheory, of which the various string theories and eleven dimensional supergravity are weakly coupled descriptions. In this context, it is crucial to identify and test systematically the consistency conditions that we expect quantum theories of gravity to satisfy.
In this project, we investigated a type of consistency conditions which has not yet been explored thoroughly: the cancellation of global gravitational anomalies in the effective field theory to which the quantum gravity theory reduces at low energies. Global gravitational anomalies are a subtle breaking of the invariance of the quantum field theory partition function under the action of the group of diffeomorphisms. Such a breaking impedes the gauging of the metric and in consequence cannot occur if the quantum field theory is obtained as a low energy limit of a consistent theory of quantum gravity. The cancellation of global gravitational anomalies is familiar to many theoretical physicists in the case of twodimensional conformal field theories, where it goes under the name of modular invariance.
In the latter case, one often can find closed expressions for the partition function of the quantum field theory, what allows to study the anomaly with modular forms. This is not the case in general and we have to use more elaborate mathematical techniques. We see the partition function as the section of a line bundle over the space of metrics modulo diffeomorphisms, the anomaly bundle. Although the partition function is often too complicated to study directly, one can often define a natural connection on the anomaly bundle. By studying this connection, one can determine if the partition function can be defined as a true function over the space of metrics modulo diffeomorphisms. More precisely, all of the holonomies of the connection must be trivial. This is the condition of vanishing of the global gravitational anomaly.
In the supergravity, string theory and Mtheory context, there are essentially two types of chiral quantum field theories which can give rise to gravitational anomalies. The first are chiral fermionic field theories, for which an anomaly formula has been known since the mid80's. The other are selfdual abelian gauge field theories, for which a complete anomaly formula was not known.
Our contribution has been to determine a formula for the global gravitational anomaly of the selfdual field theories.
Mathematically, our derivation features a beautiful mix of different mathematical subjects: index theory, modular geometry and algebraic topology. There is no doubt that there is a rich mathematical structure underlying it and remaining to be uncovered. Some of these mathematical aspects have already been explored in a publication and yielded a new topological invariant of spin manifolds.
Physically, we have only begun to explore the many situations in which we can now check the cancellation of global gravitational anomalies and test our current understanding of supergravity, string theory and Mtheory. We already managed to check the cancellation of global gravitational anomalies in a certain version of type IIB supergravity. Forthcoming work will explore the cancellation in the version of type IIB supergravity describing the low energy limit of the type IIB superstring, in six dimensional supergravities and for the worldvolume theories of the fivebranes in Mtheory, type IIA string theory and heterotic strings. Given all we already learned about quantum field theory, supergravity and string theory from anomalies, we can hope that the cancellation of global gravitational anomalies will provide us with further decisive insights into these theories and the nature of quantum gravity.
Project information
D2DFT
Grant agreement ID: 254456
Status
Closed project

Start date
1 September 2010

End date
31 August 2012
Funded under:
FP7PEOPLE

Overall budget:
€ 157 945,60

EU contribution
€ 157 945,60
Deliverables
Deliverables not available
Publications
Project information
D2DFT
Grant agreement ID: 254456
Status
Closed project

Start date
1 September 2010

End date
31 August 2012
Funded under:
FP7PEOPLE

Overall budget:
€ 157 945,60

EU contribution
€ 157 945,60
Project information
D2DFT
Grant agreement ID: 254456
Status
Closed project

Start date
1 September 2010

End date
31 August 2012
Funded under:
FP7PEOPLE

Overall budget:
€ 157 945,60

EU contribution
€ 157 945,60