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Abstract

Conformal Field Theories (CFTs) play a pivotal role in various areas of theoretical physics, including string theory, holography, and condensed matter physics. Many of these theories feature non-local excitations, known as defects. Conformal defects break some of the conformal symmetry of the bulk theory while preserving it on the defect. Therefore, it is natural to study them using similar methods to those employed for CFTs without defects, such as the analytic conformal bootstrap. In this thesis, we develop some analytic bootstrap techniques specifically for defect CFTs. We also apply these techniques to several defects that are relevant in the context of condensed matter physics or holography. We begin by reviewing the fundamental principles of conformal field theory and the analytic bootstrap. Following this, we derive dispersion relations that enable the reconstruction of defect and bulk correlators from their singularities. In favorable cases, these singularities are determined by a small set of data of defect and bulk operators. Specifically, we derive a new dispersion relation which computes the four-point function of defect operators in 1d CFTs (i.e. line defects) as an integral over its double discontinuity. Additionally, we construct two distinct dispersion relations for two-point functions of bulk operators in presence of a defect. The first one expresses the correlator as an integral over a single discontinuity governed by the bulk channel Operator Product Expansion (OPE). The second relation reconstructs the correlator from a double discontinuity controlled by the defect channel OPE. We also derive a different dispersion relation for the special case of codimension-one defects. In the last part of the thesis, we analyze the O(N) model in presence of line defects, which correspond to magnetic impurities in condensed matter systems. In particular, using a dispersion relation, we compute the two-point function of the fundamental field at the first non-trivial order in the ε-expansion. From this result, we are able to extract an infinite set of new defect CFT data. Finally, we compute holographic correlators in presence of the supersymmetric Wilson line in N = 4 Super Yang-Mills. Using the dispersion relation, we compute the four-point function of defect operators up to fourth order in the large t’Hooft coupling expansion. Our derivation validates the results previously obtained using an Ansatz. Similarly, we streamline the computation of twopoint functions of half-BPS single trace bulk operators, thanks to the efficiency of the dispersion relation.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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