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Conformal Defects in Two-Dimensional Conformal Field Theories

Student thesis: Doctoral ThesisDoctor of Philosophy

We study conformal defects in two-dimensional conformal field theories (CFTs). These are one-dimensional objects across which the difference between the holomorphic and antiholomorphic parts of the stress-energy tensor is continuous. Such defects may exist within a CFT as well as between two different CFTs. There are two subclasses of conformal defects that are well-known: topological defects, which preserve the holomorphic and antiholomorphic parts of the stress-energy tensor separately, and factorising defects, which can be considered as products of conformal boundary conditions separating the theory along the defect. In this thesis, we call conformal defects, which do not fall into either of the aforementioned subclasses, non-trivial conformal defects.
The primary focus of this thesis is studying the non-trivial conformal defect present in a unitary Virasoro minimal model which was first predicted by Kormos, Runkel, and Watts [98]. As a first step, we calculate the reflection and transmission coefficients, which were first defined in [91], of these defects using the leading-order perturbative calculation. We then consider conformal defects in the tri-critical Ising model as a concrete example. We revisit the construction of super-conformal defects proposed by Gang and Yamaguchi [94] and give a more systematic construction of such defects using super W-algebras. In addition, we propose a topological interface separating the super-conformal and bosonic theories, from which conformal defects in the latter theory can be obtained from the former one. Using the topological interfaces and superconformal defects, we obtain non-topological and non-factorising defects in the bosonic tri-critical Ising model.
Original languageEnglish
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Award date2018

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