Matris ayar teorilerinin simetrik indirgenmesi ve kaotik dinamiği.

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Fizik Bölümü, Türkiye

Tezin Onay Tarihi: 2018

Tezin Dili: İngilizce

Öğrenci: Göksu Can Toğa

Danışman: SEÇKİN KÜRKCÜOĞLU

Özet:

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