Related papers: Conformal invariance and Renormalization Group
In the first part, we concentrate on CFTs in coordinate space. We lay the foundations of Conformal Field Theory and we also demonstrate a method where by using the embedding formalism we can derive up to n-point scalar conformal…
Recent years witnessed an extensive development of the theory of the critical point in two-dimensional statistical systems, which allowed to prove {\it existence} and {\it conformal invariance} of the {\it scaling limit} for two-dimensional…
Rank-d Tensorial Group Field Theories are quantum field theories defined on a group manifold $G^{\times d}$, which represent a non-local generalization of standard QFT, and a candidate formalism for quantum gravity, since, when endowed with…
We consider two-dimensional chiral, first-order conformal field theories governing maps from the Riemann sphere to the projective light cone inside Minkowski space -- the natural setting for describing conformal field theories in two fewer…
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)…
Recently introduced ''fuzzy sphere'' method has enabled accurate numerical regularizations of certain three-dimensional (3D) conformal field theories (CFTs). The regularization is provided by the non-commutative geometry of the lowest…
We derive universal constraints on $(1+1)d$ rational conformal field theories (CFTs) that can arise as transitions between topological theories protected by a global symmetry. The deformation away from criticality to the trivially gapped…
Massive fields on anti-de Sitter (AdS) space enjoy galileon-like shift symmetries at particular values of their masses. We explore how these shift symmetries are realized through the boundary conformal field theory (CFT), at the level of…
We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that…
Conformal field theories (CFTs) in Euclidean signature satisfy well-accepted rules, such as conformal invariance and the convergent Euclidean operator product expansion (OPE). Nowadays, it is common to assume that CFT correlators exist and…
Path integrals have played a fundamental role in emphasizing the profound analogies between Quantum Field Theory (QFT), and Classical as well as Quantum Statistical Physics. Ideas coming from Statistical Physics have then led to a deeper…
Boundaries not only are fundamental elements in nearly all realistic physical systems, but also greatly enrich the structure of quantum field theories. In this paper, we demonstrate that conformal field theory (CFT) with a boundary, known…
We propose a connection between conformal field theory (CFT) and the exact solution and integrability of the reduced BCS model of superconductivity. The relevant CFT is given by the $SU(2)_k$-WZW model in the singular limit when the level k…
The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory. This is easier than directly solving the…
The fuzzy-sphere regularisation is a powerful tool to study conformal field theories (CFT) in three spacetime dimensions. In this paper, we extend its scope to CFTs with local fermionic operators. We realise the free-Majorana-fermion CFT on…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
We explore the application of the nonperturbative functional renormalization group (NPFRG) within its most common approximation scheme based on truncations of the derivative expansion, to the $Z_2$-symmetric scalar $\varphi^4$ theory as the…
For QFTs in AdS the boundary correlation functions remain conformal even if the bulk theory has a scale. This allows one to constrain RG flows with numerical conformal bootstrap methods. We apply this idea to flows between two-dimensional…
The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on…
This thesis comprises two parts centered around the functional renormalization-group framework: in the first part, I study the role of symmetries and conservation laws in approximate solutions, while in the second part I analyze Friedel…