Related papers: Defects in scalar field theories, RG flows and Dim…

Defects are both physically rich objects and powerful tools in modern quantum field theory. They are extended operators, such as boundaries, impurities, and probe particles, embedded in many-body systems. In this dissertation, we study the…

We employ perturbative RG and $\epsilon$-expansion to study multi-critical single-scalar field theories with higher derivative kinetic terms of the form $\phi(-\Box)^k\phi$. We focus on those with a $\mathbb{Z}_2$-symmetric critical point…

We study the two-dimensional version of a quartic self-interacting quantum scalar field on a curved and noncommutative space (Snyder-de Sitter). We show that the model is renormalizable at the one-loop level and compute the beta functions…

We propose defect lines as a useful tool to study bulk perturbations of conformal field theories, in particular to analyse the induced renormalisation group flows of boundary conditions. As a concrete example we investigate bulk…

Surface operators are among the most important observables of the 6d $\mathcal{N} = (2,0)$ theory. Here we apply the tools of defect CFT to study local operator insertions into the 1/2-BPS plane. We first relate the 2-point function of the…

Unparticles charged under a gauge group can contribute to the running of the gauge coupling. We show that a scalar unparticle of scaling dimension d contributes to the \beta function a term that is (2-d) times that from a scalar particle in…

We obtain the $\beta$-functions for the two dimensionless couplings of a 4d renormalizable scalar field theory with cubic and quartic 4-derivative interactions. Both couplings can be asymptotically free in the UV, and in some cases also in…

We study three-point functions of operators on the $1/2$ BPS Wilson loop in planar $\mathcal{N}=4$ super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We…

The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel…

We analyze renormalization group (RG) flows in two-dimensional quantum field theories in the presence of redundant directions. We use the operator picture in which redundant operators are total derivatives. Our analysis has three levels of…

The gradient property of the renormalisation group (RG) is examined to four-loop order in scalar-fermion systems in $d=4$ and $d=4-\varepsilon$ dimensions. The crucial role played by the beta shift, which is a modification of the standard…

We study various aspects of codimension one defects in free scalar field theory, with particular emphasis on line defects in two-dimensions. These defects are generically non-conformal, but include conformal and topological defects as…

Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave…

We consider the double-scaling limit in matrix models for two-dimensional quantum gravity, and establish the nonperturbative functional Renormalization Group as a novel technique to compute the corresponding interacting fixed point of the…

A scalar theory can have many Gaussian (free) fixed points, corresponding to Lagrangians of the form $\phi\,\Box^k\phi$. We use the non-perturbative RG to study examples of flows between such fixed points. We show that the anomalous…

We continue our study of renormalization group (RG) flows on Wilson loop defects in ABJM theory, which we have initiated in arXiv:2211.16501. We generalize that analysis by including non-supersymmetric fixed points and RG trajectories. To…

We investigate $\beta$-functions of quantum gravity using dimensional regularisation. In contrast to minimal subtraction, a non-minimal renormalisation scheme is employed which is sensitive to power-law divergences from mass terms or…

In this paper we study the constraints imposed by conformal invariance on extended objects a.k.a defects in a conformal field theory. We identify a particularly nice class of defects that is closed under conformal transformations.…

The most general version of a renormalizable $d=4$ theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains $12$ independent functions, which…

We study the two-point function of local operators in the presence of a defect in a generic conformal field theory. We define two pairs of cross ratios, which are convenient in the analysis of the OPE in the bulk and defect channel…