Fuzzy Geometry and the Quantum M-Theory Super-Fivebrane

Lead Research Organisation: University of Cambridge
Department Name: Applied Maths and Theoretical Physics


In the 19th century the impressionist painters invented a new style of painting. Actually, there were two schools of impressionist painters, with very different philosophies. One school was the `pointillists'. If you look closely at a pointillist painting you'll see that it is constructed from individual dots of colour that are bit like 'atoms' of paint. The other school of impressionist painters--let's call them the 'ondulists'--painted in a very different way. From afar, an ondulist painting may look similar to a pointillist painting, but if you look closely you see just a vague wash of brushstrokes. No dots.Any ordinary material has a structure analogous to a pointillist painting. It may appear continuous, but will betray its atomic nature under sufficiently powerful magnification. Could there be extra-ordinary materials that are analogous to an ondulist painting? Well, there is a physical analogy of the ondulists' method: holography. A laser holograph is a piece of film through which laser light is shone to produce a 3D image. An equally remarkable property of a holograph is that any small part of it can be used to produce the entire image! If the negative of an ordinary photograph is cut in half, and one half discarded, then one has lost half the image. Not so with a laser holograph; the whole image is still there, but fuzzier.The word material suggests something substantial, but modern physics, based on the ideas of quantum mechanics and Einstein's theory of 'general relativity', views even the vacuum as a kind of material--let's call it spacetime . Quantum mechanics, which tells us how the atoms of ordinary materials behave, also tells us that spacetime should have a 'quantum' structure. Until recently, we were pointillists, imagining some kind of atomic structure, but now our best theories hint that Nature is an ondulist, and that holography is the appropriate metaphor. My aim is to elucidate the fuzzy nature of quantum spacetime, and work out its consequences for the physical world, via what is called 'M-theory'.In M-theory, the basic building blocks for matter are branes , which is a generic term derived from membranes for an extended object. M theory is not yet a true theory, but rather a collection of interlocking view points, in each of which one brane is dominant. From one such view point, M theory appears to be a theory of fivebranes . I aim to understand how this perspective may lead to a theory of quantum spacetime.


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Andringa R (2010) Massive 3D supergravity in Classical and Quantum Gravity

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Bandos I (2008) Light-cone M5 and multiple M2-branes in Classical and Quantum Gravity

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Bergshoeff E (2011) More on massive 3D supergravity in Classical and Quantum Gravity

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Bergshoeff E (2010) On maximal massive 3D supergravity in Classical and Quantum Gravity

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Bergshoeff E (2011) More on massive 3D supergravity in Classical and Quantum Gravity

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Bergshoeff EA (2009) Massive gravity in three dimensions. in Physical review letters

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Bergshoeff EA (2006) Open M5-branes. in Physical review letters

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Gibbons G (2006) Self-gravitating Yang monopoles in all dimensions in Classical and Quantum Gravity

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Hohm O (2012) On the Hamiltonian form of 3D massive gravity in Physical Review D

Description I found various surprising features of ``fivebranes'' which play a key role in the unification of superstring theories of gravity and
the other forces of nature. I completed a mathematical study
in which ``fuzzy geometry'' was applied to model electrons confined to a plane or a sphere and constrained by ``supersymmetry''. It has questioned recently whether the graviton (quantum of the gravitational field) could have a non-zero mass; I found a simple model which shows that the answer is yes in a space of only two, rather than three, dimensions.
Exploitation Route A competing group in Japan developed ``fuzzy geometry'' models for electrons on planar surfaces in parallel with my work; they are still pursuing this (and citing my work) for its possible application to condensed matter physics. My work on ``massive gravity'' in 3D was soon generalised to 4D, where it has potential applications to cosmology.
Sectors Education,Other

Description My work has been used, or had some influence on, many others working on related topics, as is shown by the fact that my papers (related to this award) have been cited about 1000 times.
First Year Of Impact 2006
Sector Other
Impact Types Cultural

Description Bandos 
Organisation University of the Basque Country
Country Spain 
Sector Academic/University 
PI Contribution Discussion and collaboration on joint projects
Collaborator Contribution Collaboration was with Igor Bandos.
Impact Two publications with Bandos. Invitation from Ikerbasque to deliver popular talk at a museum in Bilbao.
Start Year 2007
Description Groningen 
Organisation University of Groningen
Country Netherlands 
Sector Academic/University 
PI Contribution Multiple visits of myself to Groningen to work with Prof. E. Bergshoeff
Collaborator Contribution Discussions and joint work on various projects.
Impact 10 publications
Start Year 2006
Description Luca Mezincescu 
Organisation University of Miami
Country United States 
Sector Academic/University 
PI Contribution Discussion and calculation on joint projects
Collaborator Contribution Discussion and calculation on joint projects
Impact 12 publications
Start Year 2008
Description Talk in Bilbao museum, Spain, with title La Gravedad de lo Diminuto y de lo Inmenso 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Public/other audiences
Results and Impact There was an extended question an answer session in which I discussed points raised by members of the audience

None that I am aware of
Year(s) Of Engagement Activity 2010