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You searched for subject:( epsilon expansion). Showing records 1 – 3 of 3 total matches.

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Princeton University

1. Tarnoplskiy, Grigory M. Conformal and Nearly Conformal Theories at Large N .

Degree: PhD, 2017, Princeton University

In this thesis we present new results in conformal and nearly conformal field theories in various dimensions. In chapter two, we study different properties of the conformal Quantum Electrodynamics (QED) in continuous dimension d. At first we study conformal QED using large Nf methods, where Nf is the number of massless fermions. We compute its sphere free energy as a function of d, ignoring the terms of order 1/Nf and higher. For finite Nf we use the -expansion. Next we use a large Nf diagrammatic approach to calculate the leading corrections to CT, the coefficient of the two-point function of the stress-energy tensor, and CJ, the coefficient of the two-point function of the global symmetry current. We present explicit formulae as a function of d and check them versus the expectations in 2 and 4-epsilon dimensions. In chapter three, we discuss vacuum stability in 1+1 dimensional conformal field theories with external background fields. We show that the vacuum decay rate is given by a non-local two-form. This two-form is a boundary term that must be added to the effective in/out Lagrangian. The two-form is expressed in terms of a Riemann-Hilbert decomposition for background gauge fields, and is given by its novel ``functional'' version in the gravitational case. In chapter four, we explore Tensor models. Such models possess the large N limit dominated by the melon diagrams. The quantum mechanics of a real anti-commuting rank-3 tensor has a large N limit similar to the Sachdev-Ye-Kitaev (SYK) model. We also discuss the quantum mechanics of a complex 3-index anti-commuting tensor and argue that it is equivalent in the large N limit to a version of SYK model with complex fermions. Finally, we discuss models of a commuting tensor in dimension d. We study the spectrum of the large N quantum field theory of bosonic rank-3 tensors using the Schwinger-Dyson equations. We compare some of these results with the 4-epsilon expansion, finding perfect agreement. We also study the spectra of bosonic theories of rank q-1 tensors with phi^q interactions. Advisors/Committee Members: Klebanov, Igor R (advisor), Polyakov, Alexander M (advisor).

Subjects/Keywords: Conformal Field Theory; epsilon expansion; Large N expansion; Quantum Field Theory

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APA (6th Edition):

Tarnoplskiy, G. M. (2017). Conformal and Nearly Conformal Theories at Large N . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01zc77ss769

Chicago Manual of Style (16th Edition):

Tarnoplskiy, Grigory M. “Conformal and Nearly Conformal Theories at Large N .” 2017. Doctoral Dissertation, Princeton University. Accessed September 15, 2019. http://arks.princeton.edu/ark:/88435/dsp01zc77ss769.

MLA Handbook (7th Edition):

Tarnoplskiy, Grigory M. “Conformal and Nearly Conformal Theories at Large N .” 2017. Web. 15 Sep 2019.

Vancouver:

Tarnoplskiy GM. Conformal and Nearly Conformal Theories at Large N . [Internet] [Doctoral dissertation]. Princeton University; 2017. [cited 2019 Sep 15]. Available from: http://arks.princeton.edu/ark:/88435/dsp01zc77ss769.

Council of Science Editors:

Tarnoplskiy GM. Conformal and Nearly Conformal Theories at Large N . [Doctoral Dissertation]. Princeton University; 2017. Available from: http://arks.princeton.edu/ark:/88435/dsp01zc77ss769


Princeton University

2. Fei, Lin. Conformal Field Theories in the Epsilon and 1/N Expansions .

Degree: PhD, 2017, Princeton University

In this thesis, we study various conformal field theories in two different approximation schemes - the epsilon-expansion in dimensional continuation, and the large N expansion. We first propose a cubic theory in d=6-epsilon as the UV completion of the quartic scalar O(N) theory in d>4. We study this theory to three-loop order and show that various operator dimensions are consistent with large-N results. This theory possesses an IR stable fixed point at real couplings for N>1038, suggesting the existence of a perturbatively unitary interacting O(N) symmetric CFT in d=5. Extending this model to Sp(N) symmetric theories, we find an interacting non-unitary CFT in d=5. For the special case of Sp(2), the IR fixed point possesses an enhanced symmetry given by the supergroup OSp(1|2). We also observe that various operator dimensions of the Sp(2) theory match those from the 0-state Potts model. We provide a graph theoretic proof showing that the zero, two, and three-point functions in the Sp(2) model and the 0-state Potts model indeed match to all orders in perturbation theory, strongly suggesting their equivalence. We then study two fermionic theories in d=2+epsilon - the Gross-Neveu model and the Nambu-Jona-Lasinio model, together with their UV completions in d=4-epsilon given by the Gross-Neveu-Yukawa and the Nambu-Jona-Lasinio-Yukawa theories. We compute their sphere free energy and certain operator dimensions, passing all checks against large-N results. We use two sided Pad\'e approximations with our epsilon expansion results to obtain estimates of various quantities in the physical dimension d=3. Finally, we provide evidence that the N=1 Gross-Neveu-Yukawa model which contains a 2-component Majorana fermion, and the N=2 Nambu-Jona-Lasinion-Yukawa model which contains a 2-component Dirac fermion, both have emergent supersymmetry. Advisors/Committee Members: Giombi, Simone (advisor).

Subjects/Keywords: conformal field theory; epsilon expansion; large N expansion; O(N); Potts; supersymmetry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Fei, L. (2017). Conformal Field Theories in the Epsilon and 1/N Expansions . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp0144558g94m

Chicago Manual of Style (16th Edition):

Fei, Lin. “Conformal Field Theories in the Epsilon and 1/N Expansions .” 2017. Doctoral Dissertation, Princeton University. Accessed September 15, 2019. http://arks.princeton.edu/ark:/88435/dsp0144558g94m.

MLA Handbook (7th Edition):

Fei, Lin. “Conformal Field Theories in the Epsilon and 1/N Expansions .” 2017. Web. 15 Sep 2019.

Vancouver:

Fei L. Conformal Field Theories in the Epsilon and 1/N Expansions . [Internet] [Doctoral dissertation]. Princeton University; 2017. [cited 2019 Sep 15]. Available from: http://arks.princeton.edu/ark:/88435/dsp0144558g94m.

Council of Science Editors:

Fei L. Conformal Field Theories in the Epsilon and 1/N Expansions . [Doctoral Dissertation]. Princeton University; 2017. Available from: http://arks.princeton.edu/ark:/88435/dsp0144558g94m


Texas A&M University

3. Gibbons, Sean Lee. Austenite-Grain Refinement and Epsilon-Carbide Precipitation Optimization in Ultra High Strength Steel Alloy ES-1.

Degree: PhD, Materials Science and Engineering, 2016, Texas A&M University

In this work, two thermo-mechanical treatments of Eglin Steel (ES-1) are designed that leverage computational tools and focus on microstructural grain refinement and optimal epsilon-carbide (Fe2:4C) precipitation. More specifically, ES-1 is presented as a candidate for Integrated Computational Materials Science and Engineering (ICME) optimization, highlighting key areas of desired improvement (e.g., tensile strength, hardness, and toughness). The two primary areas addressed throughout this work are optimal epsilon-carbide precipitation strengthening and parent austenite grain refinement. The methods used to assess and improve both parameters are outlined. Initially, the current state of ES-1 is outlined in terms of processing, microstructure, properties, and performance. It is then shown that the epsilon-carbide ground state crystal structure can be determined through a combination of first principle calculations and cluster expansions, which allows for the calculation and comparison of the ground state free energy surfaces of the various crystal structures proposed in literature. The ground state configuration of the most representative crystal structure is then used as the basis for Monte Carlo simulations to determine the finite temperature free energy surface. It is further shown that the epsilon-carbide free energy information can be coupled with existing thermodynamic and kinetic databases in order to develop a thermodynamically self-consistent phase field model (PFM) for the precipitation of epsilon-carbide. The PFM prognostic equations are outlined and methods for parallelization and evaluation are discussed. The model is then used to simulate the precipitation of epsilon-carbide at 470 K and the results are compared against experimental findings, showing good qualitative agreement. It is also shown that the precipitation of epsilon-carbide can be potentially optimized by using the PFM method in conjunction with derived system thermodynamics to develop epsilon-carbide precipitation process maps. Leveraging existing kinetic and thermodynamic databases, the remaining carbide precipitation sequences (i.e., Fe3C, M23C6, M6C, and VC) are mapped, creating a robust precipitation map of ES-1. Selected tempering regimes are experimentally assessed and used for verification of the epsilon-carbide process map. Furthermore, CALPHAD software is used to assess the thermodynamic stability of austenite in ES-1 in order to determine equal channel angular pressing (ECAP) procedures to refine parent austenite grain sizes, prior to transforming to martensite. Ultimately, this work shows that through the application of a proper thermo-mechanical treatment that the properties and performance of ES-1 and similar alloys can be significantly improved and/or tailored. Advisors/Committee Members: Arroyave, Raymundo (advisor), Karaman, Ibrahim (committee member), Amato, Nancy (committee member), Radovic, Miladin (committee member), Abrahams, Rachel (committee member).

Subjects/Keywords: epsilon-carbide; UHSS; DFT; Phase Field Modeling; Eglin Steel; cluster expansion; Precipitation Process Maps; ECAP; Austenite Grain Refinement

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Gibbons, S. L. (2016). Austenite-Grain Refinement and Epsilon-Carbide Precipitation Optimization in Ultra High Strength Steel Alloy ES-1. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/156891

Chicago Manual of Style (16th Edition):

Gibbons, Sean Lee. “Austenite-Grain Refinement and Epsilon-Carbide Precipitation Optimization in Ultra High Strength Steel Alloy ES-1.” 2016. Doctoral Dissertation, Texas A&M University. Accessed September 15, 2019. http://hdl.handle.net/1969.1/156891.

MLA Handbook (7th Edition):

Gibbons, Sean Lee. “Austenite-Grain Refinement and Epsilon-Carbide Precipitation Optimization in Ultra High Strength Steel Alloy ES-1.” 2016. Web. 15 Sep 2019.

Vancouver:

Gibbons SL. Austenite-Grain Refinement and Epsilon-Carbide Precipitation Optimization in Ultra High Strength Steel Alloy ES-1. [Internet] [Doctoral dissertation]. Texas A&M University; 2016. [cited 2019 Sep 15]. Available from: http://hdl.handle.net/1969.1/156891.

Council of Science Editors:

Gibbons SL. Austenite-Grain Refinement and Epsilon-Carbide Precipitation Optimization in Ultra High Strength Steel Alloy ES-1. [Doctoral Dissertation]. Texas A&M University; 2016. Available from: http://hdl.handle.net/1969.1/156891

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