Related papers: Bootstrapping $\mathcal{N}=3$ superconformal theor…
We analyze the conformal bootstrap constraints in theories with four supercharges and a global $O(N) \times U(1)$ flavor symmetry in $3 \leq d \leq 4$ dimensions. In particular, we consider the 4-point function of $O(N)$-fundamental chiral…
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
We study two-dimensional (4,4) superconformal field theories of central charge c=6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the…
We study 2d N=4 superconformal field theories, focusing on its application on numerical bootstrap study. We derive the superconformal block by utilizing the global part of the super Virasoro algebra and set up the crossing equations for the…
Applications of the bootstrap program to superconformal field theories promise unique new insights into their landscape and could even lead to the discovery of new models. Most existing results of the superconformal bootstrap were obtained…
The chiral algebra of a 4D $N\geq2$ superconformal field theory is a vertex operator algebra generated by the Schur subsector of the 4D theory and its rigid (yet rich) structure has been useful in constraining and classifying 4D N=2 SCFTs.…
The recent emergence of the modern conformal bootstrap method for the study of conformal field theories (CFTs) has enabled the revisiting of old problems in classical critical phenomena described by three-dimensional CFTs. The study of such…
Using the numerical modular bootstrap, we constrain the space of 1+1d CFTs with a finite non-invertible global symmetry described by a fusion category $\mathcal{C}$. We derive universal and rigorous upper bounds on the lightest…
Conformal field theories (CFTs) with $U(m)\times U(n)$ global symmetry in $d=3$ dimensions have been studied for years due to their potential relevance to the chiral phase transition of quantum chromodynamics (QCD). In this work such CFTs…
We implement the conformal bootstrap for N=4 superconformal field theories in four dimensions. Consistency of the four-point function of the stress-energy tensor multiplet imposes significant upper bounds for the scaling dimensions of…
We find a simple relation between two-dimensional BPS N=2 superconformal blocks and bosonic Virasoro conformal blocks, which allows us to analyze the crossing equations for BPS 4-point functions in unitary (2,2) superconformal theories…
6d (2,0) SCFTs of type $\mathfrak{g}$ have protected subsectors that were conjectured in arxiv:1404.1079 to be captured by $\mathcal{W}_\mathfrak{g}$ algebras. We write down the crossing equations for mixed four-point functions $\langle…
Conformal field theories (CFTs) with MN and tetragonal global symmetry in $d=2+1$ dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions in a wide class of materials. The study of these theories with…
We study the consistency of four-point functions of half-BPS chiral primary operators of weight p in four-dimensional N=4 superconformal field theories. The resulting conformal bootstrap equations impose non-trivial bounds for the scaling…
We consider the embedding method of the superconformal group in four dimensions in the case of extended supersymmetry, hence generalizing the recent work of Goldberger, Skiba and Son which was restricted at N=1. Moreover, we work out…
Genus two partition functions of 2d chiral conformal field theories are given by Siegel modular forms. We compute their conformal blocks and use them to perform the conformal bootstrap. The advantage of this approach is that it imposes…
We propose a construction of the quantum-corrected Coulomb branch of a general 3d gauge theory with $\mathcal{N}=4$ supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the…
We study analytically the constraints of the conformal bootstrap on the low-lying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals…
In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic…
We study the conformal bootstrap for systems of correlators involving non-identical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We…