Dimensional deconstruction
Encyclopedia
In theoretical physics
, dimensional deconstruction is a method to construct d-dimensional theories that behave as higher-dimensional theories in a certain range of energies. The resulting theory is a gauge theory
whose gauge group is a direct product
of many copies of the same group; each copy may be interpreted as the gauge group located at a particular point along a new, discrete, "deconstructed" (d+1)st dimension. The spectrum of matter fields is a set of bifundamental representation
s expressed by a quiver diagram
that is analogous to lattices in lattice gauge theory
.
"Deconstruction" in physics was introduced by Nima Arkani-Hamed
, Andy Cohen and Howard Georgi
, and independently by Christopher T. Hill
, Stefan Pokorski and Jing Wang
. The latter authors viewed the method as a lattice approximation to the real space of extra dimensions, while maintaining the full gauge symmetries to obtain the low energy effective description of the physics. This leads to a rationale for extensions of the Standard Model based upon product gauge groups,
, such as anticipated in
"topcolor
" models of electroweak symmetry breaking.
The little Higgs
theories are also examples of phenomenologically interesting theories inspired by deconstruction.
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, dimensional deconstruction is a method to construct d-dimensional theories that behave as higher-dimensional theories in a certain range of energies. The resulting theory is a gauge theory
Gauge theory
In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
whose gauge group is a direct product
Direct product of groups
In the mathematical field of group theory, the direct product is an operation that takes two groups and and constructs a new group, usually denoted...
of many copies of the same group; each copy may be interpreted as the gauge group located at a particular point along a new, discrete, "deconstructed" (d+1)st dimension. The spectrum of matter fields is a set of bifundamental representation
Bifundamental representation
In mathematics and theoretical physics, a bifundamental representation is a representation obtained as a tensor product of two fundamental or antifundamental representations....
s expressed by a quiver diagram
Quiver diagram
In physics, a quiver diagram is a graph representing the matter content of a gauge theory that describes D-branes on orbifolds.Each node of the graph corresponds to a factor U of the gauge group, and each link represents a field in the bifundamental representation.The relevance of quiver diagrams...
that is analogous to lattices in lattice gauge theory
Lattice gauge theory
In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important in particle physics, and include the prevailing theories of elementary particles: quantum electrodynamics, quantum chromodynamics and the Standard...
.
"Deconstruction" in physics was introduced by Nima Arkani-Hamed
Nima Arkani-Hamed
Nima Arkani-Hamed is a leading Canadian American theoretical physicist with interests in high-energy physics, string theory and cosmology....
, Andy Cohen and Howard Georgi
Howard Georgi
Howard Mason Georgi III, born January 6, 1947 in San Bernardino, California, is Harvard College Professor and Mallinckrodt Professor of Physics at Harvard University...
, and independently by Christopher T. Hill
Christopher T. Hill
Christopher T. Hill is a theoretical physicist at the Fermi National Accelerator Laboratory. He did undergraduate work in physics at M.I.T. , and graduate work at Caltech...
, Stefan Pokorski and Jing Wang
Jing Wang
Jing Wang is Professor of Chinese media and Cultural Studies and S.C. Fang Professor of Chinese Language & Culture at Massachusetts Institute of Technology, She is soon to join MIT's Comparative Media Studies....
. The latter authors viewed the method as a lattice approximation to the real space of extra dimensions, while maintaining the full gauge symmetries to obtain the low energy effective description of the physics. This leads to a rationale for extensions of the Standard Model based upon product gauge groups,
, such as anticipated in"topcolor
Topcolor
In theoretical physics, Topcolor is a model of dynamical electroweak symmetry breaking in which the top quark and anti-top quark form a top quark condensate and act effectively like the Higgs boson. This is analogous to the phenomenon of superconductivity....
" models of electroweak symmetry breaking.
The little Higgs
Little Higgs
In particle physics, little Higgs models are based on the idea that the Higgs boson is a pseudo-Goldstone boson arising from some global symmetry breaking at a TeV energy scale...
theories are also examples of phenomenologically interesting theories inspired by deconstruction.
External links
- Littlest Higgs model and deconstruction: an introduction