Random Surfaces and Quantum Gravity

SUMMARY

Monte Carlo methods are being used to study discrete random surface models of string theory and quantum gravity. We are developing algorithms for parallelizing this dynamic irregular mesh problem.

PARTICIPATING INSTITUTIONS

NPAC, Syracuse University
Physics Department, Syracuse University

KEY CONTACTS

Mark Bowick | bowick@npac.syr.edu | 315-443-5979

Enzo Marinari | marinari@npac.syr.edu | 315-443-5976

Paul Coddington | paulc@npac.syr.edu | 315-443-4883

IMPACT

These programs are part of the HPF/F90D benchmark suite. Most of the parallel algorithms we are developing (e.g. graph coloring, graph partitioning, load balancing) are also useful in other applications such as parallel differential equation solvers, especially on unstructured adaptive meshes.

PROJECT DESCRIPTION

String theories are quantum field theories in which the fundamental particles are tiny one dimensional strings, rather than points with no dimension. There has been great interest in string theories, since they provide a long awaited quantum theory of gravity, as well as being able to reproduce the standard quantum model of the other fundamental forces of nature, and are thus a possible TOE (Theory of Everything). However string calculations are usually analytically intractible, so methods are being developed to do calculations numerically using computer simulation.

String theory calculations involve integrating over all possible two dimensional surfaces swept out by the string in some higher dimensional space-time. In order to compute this integral numerically, the surfaces are discretized as a triangulated mesh. The integral is then approximated by a sum over a large number of different meshes, which are obtained by making random changes to the mesh throughout the calculation, using a Monte Carlo method. The mesh is thus referred to as a dynamically triangulated random surface.

Currently we are running our simulations on parallel computers and networks of workstations by using the trivial parallelism of averaging the results of independent simulations on different processors. However this can only be done effectively for small meshes. We are currently working on a data parallel algorithm for larger meshes. Since both the data and the algorithm are dynamic and irregular, this is a challenging problem, which requires parallel algorithms for graph coloring, graph partitioning, load balancing, adaptive mesh generation, as well as the Monte Carlo update.

A dynamically triangulated random surface configuration for a model of 3 dimensional string theory.

REFERENCES

1. SCCS-269
   M. Bowick and E. Marinari, Quantum Gravity, Random Geometry and Critical Phenomena, Gen. Rel. Grav. 24, 1209 (1992).
2. SCCS-357
   M. Bowick, P. Coddington, L. Han, G. Harris and E. Marinari, The Phase Diagram of Fluid Random Surfaces with Extrinsic Curvature, Nucl. Phys. B 394, 791 (1993).
3. SCCS-361
   B. Bruegmann and E. Marinari, 4D Simplicial Quantum Gravity with a Nontrivial Measure, Phys. Rev. Lett. 70, 1908 (1993).
4. SCCS-511
   K. Anagnostopoulos, M. Bowick, P. Coddington, M. Falcioni, L. Han, G. Harris and E. Marinari, Fluid Random Surfaces with Extrinsic Curvature: II, Phys. Lett. B, to appear.
5. SCCS-540
   M. Bowick, M. Falcioni, G. Harris and E. Marinari, Two Ising Models Coupled to 2-Dimensional Gravity, Nucl Phys B, to appear.
6. SCCS-568
   M. Bowick, M. Falcioni, G. Harris and E. Marinari, Critical Slowing Down of Cluster Algorithms for Ising Models Coupled to 2-d Gravity, Nucl Phys B, to appear.
7. J.R. Allwright, R. Bordawekar, P.D. Coddington, K. Dincer, C.L. Martin, A Comparison of Parallel Graph Coloring Algorithms, in preparation.
8. R. Bordawekar, P.D. Coddington, K. Dincer, M. Falcioni, L. Han, E. Marinari, Parallel Algorithms for Dynamically Triangulated Random Surfaces, in preparation.