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The numerical conformal bootstrap is used to study mixed correlators in $\mathcal{N}=1$ superconformal field theories (SCFTs) in $d=4$ spacetime dimensions. Systems of four-point functions involving scalar chiral and real operators are…
We review the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are based solely on symmetries, in particular…
We use the conformal bootstrap approach to explore $5D$ CFTs with $O(N)$ global symmetry, which contain $N$ scalars $\phi_i$ transforming as $O(N)$ vector. Specifically, we study multiple four-point correlators of the leading $O(N)$ vector…
Dispersion relations are nonperturbative formulas that relate the ultraviolet and infrared behavior of an observable with wide-ranging applications applications in linear response theory, quantum field theory scattering amplitudes, and…
We define the two-dimensional $O(n)$ conformal field theory as a theory that includes the critical dilute and dense $O(n)$ models as special cases, and depends analytically on the central charge. For generic values of $n\in\mathbb{C}$, we…
We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correlation with identical scalar operators, which is manifestly symmetric under the cross-ratios $u,v$ interchange. This representation has several features in…
The paper contributes to an ongoing effort to extend the conformal bootstrap beyond its traditional focus on systems of four-point correlation functions. Recently, it was demonstrated that semidefinite programming can be used to formulate a…
In this thesis, we analyze unitary conformal field theories in three dimensional spaces by applying analytic conformal bootstrap techniques to correlation functions of non-scalar operators, in particular Majorana fermions. Via the analysis…
We describe examples of drastic truncations of conformal bootstrap equations encoding much more information than that obtained by a direct numerical approach. A three-term truncation of the four point function of a free scalar in any space…
Using numerical conformal bootstrap technology we perform a non-perturbative study of the Ising CFT and its spectrum from infinitesimal to finite values of $\varepsilon=4-d$. Exploiting the recent navigator bootstrap method in conjunction…
We consider a conformal field theory in the presence of a boundary, and explain how two-point correlators of mixed bulk-local operators can be bootstrapped by exploiting the analytical structure of the conformal blocks. This yields the…
Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier…
We study general correlation functions of various quantum field theories in the holographic setup. Following the holographic proposal, we investigate correlation functions via a geodesic length connecting boundary operators. We show that…
Whether O(N)-invariant conformal field theory exists in five dimensions with its implication to higher-spin holography was much debated. We find an affirmative result on this question by utilizing conformal bootstrap approach. In solving…
We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising…
This is the 6th paper in the series developing the formalism to manage the effective scattering theory of strong interactions. Relying on the theoretical scheme suggested in our previous publications we concentrate here on the practical…
In this work we initiate the conformal bootstrap program for ${\mathcal N}=2$ superconformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and…
In this work we apply the lightcone bootstrap to a four-point function of scalars in two-dimensional conformal field theory. We include the entire Virasoro symmetry and consider non-rational theories with a gap in the spectrum from the…
We use the conformal bootstrap to study conformal field theories with $O(N)$ global symmetry in $d=5$ and $d=5.95$ spacetime dimensions that have a scalar operator $\phi_i$ transforming as an $O(N)$ vector. The crossing symmetry of the…
Conformal field theories play a central role in theoretical physics with many applications ranging from condensed matter to string theory. The conformal bootstrap studies conformal field theories using mathematical consistency conditions…