Related papers: Perturbative Unitarity and the 4-Point Vertices in…

The Checkerboard conformal field theory is an interesting representative of a large class of non-unitary, logarithmic Fishnet CFTs (FCFT) in arbitrary dimension which have been intensively studied in the last years. Its planar Feynman…

The combination of integrability and crossing symmetry has proven to give tight non-perturbative bounds on some planar structure constants in $\mathcal{N}$=4 SYM, particularly in the setup of defect observables built on a Wilson-Maldacena…

We explain the physical role of non-perturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based…

The divergence of perturbative expansions for the vast majority of macroscopic systems, which follows from Dyson's collapse argument, prevents Feynman's diagrammatic technique from being directly used for controllable studies of strongly…

A 6-dimensional grand unified theory with the compact space having the topology of a real projective plane, i.e., a 2-sphere with opposite points identified, is considered. The space is locally flat except for two conical singularities…

Geodesic bulk diagrams were recently shown to be the geometric objects which compute global conformal blocks. We show that this duality continues to hold in $p$-adic AdS/CFT, where the bulk is replaced by the Bruhat-Tits tree, an infinite…

To unify the quantum electrodynamics (QED) under the first principle which brings the renormalization unartificially, we study Feynman diagrams in QED according to the set theory and the category theory. We add the restriction on the…

This thesis examines the correspondence between models of statistical physics and Feynman graphs of quantum field theories (QFTs) by a common property: integrability. We review integrable structures for periodic boundary conditions on both…

We present a set of example models in which the Standard Model (SM) symmetry group is extended by a new abelian symmetry. This additional symmetry appears anomalous in the effective low-energy theory; however, the anomalies cancel out when…

We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in $d=4+\epsilon$ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten…

In this paper we analyse the perturbative aspects of Chern-Simons field theories in the Coulomb gauge. We show that in the perturbative expansion of the Green functions there are neither ultraviolet not infrared divergences. Moreover, all…

We consider the planar limit of Chern-Simons theories coupled to a scalar $\phi$ in the fundamental representation of a $U(N)_k$ gauge group, at both the regular and Wilson-Fisher conformal points. These theories have one single-trace…

The straightforward supersymmetrization of the Standard Model (SM) results in a phenomenologically inconsistent theory in which Baryon number ($B$) and Lepton number ($L$) are violated by dimension 4 operators, inducing fast proton decay.…

We show that four-dimensional topological Yang-Mills theories, when suitably coupled to Higgs-like fields, admit representations in terms of massive gauge fields in a non-trivial neighborhood of the minima moduli. In the adjoint…

We develop a Feynman diagram approach to calculating correlations of the Cosmic Microwave Background (CMB) in the presence of distortions. As one application, we focus on CMB distortions due to gravitational lensing by Large Scale Structure…

Dong, Munczek and Roberts have shown how the full 3-point vertex that appears in the Schwinger-Dyson equation for the fermion propagator can be expressed in terms of a constrained function $W_1$ in massless quenched QED. However, this…

We revisit supersymmetric nonlinear sigma models on the target manifold $CP^{N-1}$ and $SO(N)/SO(N-2)\times U(1)$ in four dimensions. These models are formulated as gauged linear models, but it is indicated that the Wess-Zumino term should…

We study a set of large-$N$ tensor field theories with a rich structure of fixed points, encompassing both the melonic and prismatic CFTs observed previously in the conformal limits of other tensor theories and in the generalised…

Magnetic and superconducting instabilities in the two-dimensional t-t'-Hubbard model are discussed within a functional renormalization group approach. The fermionic four-point vertex is efficiently parametrized by means of partial…

This thesis focuses on renormalization of tensor field theories. Its first part considers a quartic tensor model with $O(N)^3$ symmetry and long-range propagator. The existence of a non-perturbative fixed point in any $d$ at large $N$ is…