Quantum topology change and large-N gauge theories

@article{Albuquerque2004QuantumTC,
  title={Quantum topology change and large-N gauge theories},
  author={Luiz C. de Albuquerque and Paulo Teotonio-Sobrinho and Sachindeo Vaidya},
  journal={Journal of High Energy Physics},
  year={2004},
  volume={2004},
  pages={024-024}
}
We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection X of N one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator D. The set of boundary conditions encodes the topology and is parameterized by unitary matrices g. A particular geometry is described by a spectral triple x(g) = (AX,X,D(g)). We define a partition function for… 

Figures from this paper

Localization of quantum topology in the presence of matter and gauge fields

In this paper a toy model of quantum topology is reviewed to study effects of matter and gauge fields on the topology fluctuations. In the model a collection of N one-dimensional manifolds is

Fluctuating Commutative Geometry

We use the framework of noncommutative geometry to define a discrete model for fluctuating geometry. Instead of considering ordinary geometry and its metric fluctuations, we consider generalized

Quantum Physics and Fluctuating Topologies: Survey

The spin-statistics connection, quantum gravity and other physical considerations suggest that classical space-time topology is not an immutable attribute and can change in quantum physics. The

References

SHOWING 1-10 OF 49 REFERENCES

Fluctuating Commutative Geometry

We use the framework of noncommutative geometry to define a discrete model for fluctuating geometry. Instead of considering ordinary geometry and its metric fluctuations, we consider generalized

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle.

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity that describes the geometry of spaces with a countable number of points, and is related to the Gaussian unitary ensemble of Hermitian matrices.

Finite quantum physics and noncommutative geometry

Universal Formula for Noncommutative Geometry Actions: Unification of Gravity and the Standard Model.

A universal formula for an action associated with a noncommutative geometry, defined by a spectral triple sA, H, Dd, is proposed, based on the spectrum of the Dirac operator, that gives an action that unifies gravity with the standard model at a very high energy scale.

String theory and noncommutative geometry

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally

Non-perturbative 3d Lorentzian quantum gravity

The phase structure of the Wick-rotated path integral in three dimensions with the aid of computer simulations is investigated, finding a whole range of the gravitational coupling constant k{sub 0} for which the functional integral is dominated by nondegenerate three-dimensional space-times.

Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change

Gravity from Dirac Eigenvalues

We study a formulation of Euclidean general relativity in which the dynamical variables are given by a sequence of real numbers λn, representing the eigenvalues of the Dirac operator on the curved