Damtp Phd Thesis, Popular School Term Paper, Best Letter Editing Site For School, Ethics Case Study Engineering/10() Department of Applied Mathematics and Theoretical Physics (DAMTP) Theses - Applied Mathematics and Theoretical Physics Of course, to look Damtp Phd Thesis for the best custom writing service available out there. This could be challenging as there are plenty of options available, Damtp Phd Thesis and not all Damtp Phd Thesis of them are equally great. Keep in mind that while a good writing service should be affordable to you, it definitely shouldn’t be the cheapest you can find/10()
View Item Apollo Home School of damtp phd thesis Physical Sciences Department of Applied Mathematics and Theoretical Physics DAMTP Damtp phd thesis - Applied Mathematics and Theoretical Physics View Item. JavaScript is disabled for your browser. Some features of this site may not work without it, damtp phd thesis.
View Usage Statistics. Conformal Boundaries, SPTs, and the Monopole-Fermion Problem. Authors Boyle Smith, Philip. Advisors Tong, David. Date Awarding Institution University of Cambridge. Qualification Doctor of Philosophy PhD. Metadata Show full item record. Citation Boyle Smith, P. Conformal Boundaries, SPTs, and the Monopole-Fermion Problem Doctoral thesis. Abstract This thesis studies boundary states in spin conformal field theories damtp phd thesis two dimensions, and their connection to the monopole-fermion problem in four dimensions, as well as to symmetry-protected topological phases in two and three dimensions.
We begin by motivating the study of conformal boundary states for 2d fermions preserving chiral symmetries. Our main motivation is the question of defining magnetic line operators in 4d chiral gauge theories. Such line operators were originally introduced by 't Hooft in the s, and have damtp phd thesis a recent upsurge in interest after their refinement by Kapustin and Seiberg, but have only ever been defined for damtp phd thesis theories without chiral fermions.
The difficulty in extending these operators to chiral theories is known as the "fermion-monopole problem". Using a 4d - 2d partial wave reduction, we show that the problem of defining magnetic lines in chiral gauge theories reduces to defining boundary states for an effective 2d theory of Dirac fermions with certain chiral symmetries. For this to be possible, damtp phd thesis, various 2d anomalies must vanish, which places constraints on the matter content of the 4d gauge theory.
Next, to obtain the boundary states, we turn to boundary conformal field theory. After a brief review of this framework, we explain its limitations in addressing the fermion-monopole problem.
Damtp phd thesis particular, while the theory is fully established for bosonic RCFTs, it has seen little to no progress for irrational CFTs, and also remains to be fully explored for fermionic RCFTs. These factors motivate the study of a particular family of boundary states preserving maximal abelian symmetries. We classify all such symmetries, damtp phd thesis, and construct all boundary states preserving them.
The most interesting part of the construction involves taking care of the normalisation of states to ensure a consistent spectrum. We show that consistency of the spectrum indeed holds, but in a nontrivial way, with the details involving lattice theory and F2-linear algebra. Next, as further exploration of our family of boundary states, we work out the structure of boundary RG flows that connect different states. The theory of boundary RG is very similar to that of bulk RG: there are boundary operators, damtp phd thesis, which can be classed as relevant or irrelevant, and relevant boundary operators drive flows to boundary states of lower Affleck-Ludwig central charge.
We derive the spectrum of boundary operators, and construct all RG flows generated by boundary operators of definite charge. We show that a consistent picture emerges by virtue of a striking dimension formula which determines the IR central charge from the UV central charge and the dimension of the perturbing operator, damtp phd thesis. Next, we return to the fermion-monopole problem, and determine which of these boundary states can serve to define magnetic line operators.
To do this, we carefully derive the full amount of chiral symmetry that is preserved by each boundary state. The result is always a maximal-rank subgroup of SO 2Nwhere N is the number of Dirac fermions, and we give a simple prescription to determine it from the data describing the boundary state.
Due to the maximal-rank property, we conclude that generic magnetic lines cannot be described by boundary states of this kind, and to find these states would require radically different techniques. Next we turn to the connection between boundary states and SPT phases. Using Fidkowski and Kitaev's example of symmetric mass generation as an example, we illustrate the mapping between 2d boundary states and 2d gapped phases, in particular the subtle way symmetries correspond under this mapping, damtp phd thesis.
We also consider how properties of 2d boundary states can encode those of 3d SPT phases. To do this, we derive criteria for when the boundary states in our family preserve certain discrete symmetries.
We make contact with the mod-8 classification of 3d SPT phases protected by a unitary Z2 symmetry by proving a simple theorem about lattices. In the final part of this thesis, we turn from boundary states for Dirac fermions to those of more general fermionic CFTs, specifically, the recently-introduced family of fermionic minimal models, which are derived by fermionising the more familiar bosonic minimal models. We construct the boundary states for these models, and explain how our results and their interpretation in terms of 2d SPTs carry over from the Dirac fermion case.
Furthermore, in order to explain certain coincidences among our results, we construct all unitary global Z2 symmetries of these models using the modular bootstrap, and compute their anomalies. The method rests upon a combinatorial conjecture which we expect to have an interpretation in terms of Fermat curves. Our results agree with other works that appeared around the same time where they overlap.
Keywords Conformal Field Theory, Boundary Conformal Field Theory, Gauge Theory, Quantum Field Theory, Magnetic Monopoles, Topological Phases, Boundary States, damtp phd thesis, Lattices, Minimal Models, Chiral Symmetry, Chiral Fermions, Callan-Rubakov Effect.
Sponsorship Cambridge Trust, The Simons Foundation. Rights Attribution-ShareAlike 4, damtp phd thesis. Recommended or similar items. Except where otherwise noted, this item's licence is described as Attribution-ShareAlike 4.
Worst PhD defense ever.
, time: 5:02
How Damtp Phd Thes to Create the Perfect Thesis Statement with Examples Thesis statements are some of the mandatory aspects of academic writing that you`ll be required to master in college. However, most students find it challenging as they have Damtp Phd We are a life-saving service for procrastinators! Our qualified experts Damtp Phd Thesis dissertation writers excel at speedy writing and can craft a perfect paper within the shortest deadline. If you have a last-minute paper, place your urgent order at any time and pick a 3, 6, 12 or 24 hour option Everyone on our professional essay writing team is an expert in academic research Damtp Phd Thesis and in APA, MLA, Chicago, Harvard citation formats. Your project arrives fully formatted and ready to submit. The research behind the writing is always % original, and the writing is
No comments:
Post a Comment