Equivariant reduction of matrix gauge theories and emergent chaotic dynamics

Toğa, Göksu Can
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


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In this thesis, conformal transformations in d and two dimensions and the results of conformal symmetry in classical and quantum field theories are reviewed. After investigating the conformal group and its algebra, various aspects of conformal invariance in field theories, like conserved charges, correlation functions and the Ward identities are discussed. The central charge and the Virasoro algebra are briefly touched upon.
Effective gauge theories from fuzzy extra dimensions
Ünal, Gönül; Kürkcüoğlu, Seçkin; Department of Physics (2016)
In this thesis, we investigate the formulation and various aspects of gauge theories with fuzzy extra dimensions. In SU (N ) gauge theories coupled to a suitable number of adjoint scalar fields, we determine a family of fuzzy vacuum configurations dynamically emerging after the spontaneously symmetry breaking of the gauge symmetry. The emergent models are conjectured to be effective U (n) (n < N ) gauge theories with fuzzy extra dimensions. Making use of the equivariant parametrization technique and focusin...
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Non-Abelian gauge theories of the Yang-Mills type
Abuhatab, Ahmed; Başkal, Sibel; Department of Physics (2003)
In this thesis, starting from the effective Lagrangians of the standard Yang-Mills, higher derivative Yang-Mills and the Chern-Simons- Yang-Mills theories, we have given the corresponding field equations and the symmetric gauge invariant energy- momentum tensors. Lagrangians containing higher derivative terms have been found useful for discussing the long lange effects of the gluon fields. A numeri cal solution is found for a spherically symmetric static gauge potential. On the other hand, Chern-Simons- Yan...
Critical points of D-dimensional extended gravities
Deser, S.; Liu, Haishan; Lue, H.; Pope, C. N.; Sisman, Tahsin Cagri; Tekin, Bayram (2011-03-17)
We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D < 4 there are in general two distinct (anti)-de Sitter vacua. We show that, for an appropriate choice of the parameters, there exists a critical point for one of the vacua, with only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have formally vanishing energy (as do black hole solutions). A further restriction of the paramet...
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.