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Manuscript Title: A vectorized code for the computation of the topological charge in SU(2) lattice gauge theory.
Authors: A.S. Kronfeld, M.L. Laursen, G. Schierholz, C. Schleiermacher, U.-J. Wiese
Program title: QUBIC
Catalogue identifier: ABHQ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 54(1989)109
Programming language: Fortran.
Computer: CRAY X-MP/48.
Operating system: COS 1.16.
Word size: 64
Keywords: Lattice gauge theory, Topology, Instantons, Fiber bundles, Characteristic classes, Second chern number, Vector processor, Particle physics, Elementary, Qcd.
Classification: 11.5.

Nature of problem:
Four-dimensional SU(N) gauge fields are characterized by a topological charge, known as the second Chern number to mathematicians. This feature, not shared by Abelian gauge fields, is conjectured to be significant for the peculiar properties of quantized nonabelian gauge theories. For example, the topology of the gauge field is known to be relevant to the resolution of the "UA(1) problem", and the role of topology in the confinement mechanism needs clarification.

Solution method:
The problem of nonabelian gauge fields is nonperturbative, and the most successful approach has been numerical simulations of the corresponding lattice gauge theory. For lattice gauge fields the topological charge can be obtained by reconstructing the underlying topological object, the coordinate bundle, from the lattice gauge field. In the case of SU(2), the algorithm of Phillips and Stone reduces the computation of the topological charge to combinatorics. The present program uses this algorithm to compute the topological charge of a NS**3 * NT hypercubic lattice; it is designed to be appended to the potential user's existing simulation programs. The test code sets up a configuration with Q=1, to assist the user in installation.

Restrictions:
(a) The lattice size parameters NS and NT must be even.
(b) The lattice must have periodic boundary conditions.
(c) The user must provide program(s) to generate a sequence of SU(2) lattice gauge fields; QUBIC then determines the topological charge.

Running time:
Compiled with CFT compiler QUBIC needs 9.14 CPU-sec on the Cray X-MP/48 to determine the topological charge of a 10**4 lattice. Despite considerable INTEGER arithmetic and several BLOCK-IF's, QUBIC attains a performance of 47 MFLOPS.