Equivariant reduction of matrix gauge theories and emergent chaotic dynamics

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2018

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Toğa, Göksu Can

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In this thesis we focus on a massive deformation of a Yang-Mills matrix gauge theory. We first layout the essential features of this model including fuzzy 4- sphere extremum of the mass deformed potential as well as its relation with string theoretic matrix models such as the BFSS model. Starting with such a model with U(4N) gauge symmetry, we determine the SU(4) equivariant fluctuations modes. We trace over the fuzzy 4-spheres at the matrix levels N = 1 6(n + 1)(n + 2)(n + 3), (n : 1; 2 : : : 5) and obtain the corresponding low energy effective actions(LEA).This reduction over fuzzy 4-sphere breaks the U(4) gauge symmetry down to U(1) × U(1), which is further broken to Z2 × Z2 by the Gauss Law constraint on the gauge fields. We solve numerically the Hamilton’s equations of motions for the corresponding phase space variables and using the latter obtain the Lyapunov exponents, from which we conclude the presence of chaotic dynamics in the LEA. Finally in the Euclidean time, we also find that the reduced LEA’s have kink solutions with topological charges in Z2 × Z2

Subject Keywords

Gauge fields (Physics)., Fuzzy systems., Matrices.

URI

http://etd.lib.metu.edu.tr/upload/12622261/index.pdf
https://hdl.handle.net/11511/27386

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

G. C. Toğa, “Equivariant reduction of matrix gauge theories and emergent chaotic dynamics,” M.S. - Master of Science, Middle East Technical University, 2018.