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Conformal field theories (CFTs) feature prominently in high-energy physics, statistical mechanics, and condensed matter. For example, CFTs govern emergent universal properties of systems tuned to quantum phase transitions, including their…
We explore some aspects of holographic dual of Boundary Conformal Field Theory (BCFT). In particular we study asymptotic symmetry of geometries which provide holographic dual of BCFTs. We also compute two-point functions of certain bosonic…
We demonstrate that various aspects of Conformal Field Theory are amenable to machine learning. Relatively modest feed-forward neural networks are able to distinguish between scale and conformal invariance of a three-point function and…
In this work we report on a new bootstrap method for quantum mechanical problems that closely mirrors the setup from conformal field theory (CFT). We use the equations of motion to develop an analogue of the conformal block expansion for…
Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and OPE coefficients for several 3D universality classes. We show how to use this information to obtain similarly…
We study the 1d Ising model with long-range interactions decaying as $1/r^{1+s}$. The critical model corresponds to a family of 1d conformal field theories (CFTs) whose data depends nontrivially on $s$ in the range $1/2\leq s\leq 1$. The…
We study a three dimensional conformal field theory in terms of its partition function on arbitrary curved spaces. The large $N$ limit of the nonlinear sigma model at the non-trivial fixed point is shown to be an example of a conformal…
We study the effects of symmetry-breaking defects at continuous quantum transitions (CQTs), which may arise from localized external fields coupled to the order-parameter operator. The problem is addressed within renormalization-group (RG)…
We study a surface defect in the free and critical $O(N)$ vector models, defined by adding a quadratic perturbation localized on a two-dimensional subspace of the $d$-dimensional CFT. We compute the beta function for the corresponding…
In large part, the future utility of modern numerical conformal bootstrap depends on its ability to accurately predict the existence of hitherto unknown non-trivial conformal field theories (CFTs). Here we investigate the extent to which…
We initiate the analytical functional bootstrap study of conformal field theories with large $N$ limits. In this first paper we particularly focus on the 1D $O(N)$ vector bootstrap. We obtain a remarkably simple bootstrap equation from the…
We propose that scaling dimensions of d=3 conformal field theories can be studied on a system of qubits with near term quantum simulation platforms. Our proposal chooses couplings of quantum many-body problems on a polyhedral lattice at…
We introduce a new approach to the study of the crossing equation for CFTs in the presence of a boundary. We argue that there is a basis for this equation related to the generalized free field solution. The dual basis is a set of linear…
We demonstrate that simple feed-forward neural networks (NNs) can accurately compute correlation functions of conformal field theories (CFTs) on a line. Strikingly, by optimising a NN solely on crossing symmetry and providing only the…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
In a recent paper, Clusel and Fortin [J. Phys. A.: Math. Gen. 39 (2006) 995] presented an analytical study of a first-order transition induced by an inhomogeneous boundary magnetic field in the two-dimensional Ising model. They identified…
This is the first in a series of articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here, we introduce spaces of…
We study the physics of 2 and 3 mutually intersecting conformal defects forming wedges and corners in general dimension. For 2 defects we derive the beta function of the edge interactions for infinite and semi-infinite wedges and study them…
Recently, the conformal-bootstrap has been successfully used to obtain generic bounds on the spectrum and OPE coefficients of unitary conformal field theories. In practice, these bounds are obtained by assuming the existence of a scalar…
We propose a roadmap for bootstrapping conformal field theories (CFTs) described by gauge theories in dimensions $d>2$. In particular, we provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap…