Related papers: Trans-series from condensates in the non-linear si…
The scheme previously proposed by the present authors is modified to incorporate the strong interaction by affording the direct product internal symmetry. We do not need to prepare the extra discrete space for the color gauge group…
We formulate the Lagrangian perturbation theory to solve the non-linear dynamics of self-gravitating fluid within the framework of the post-Newtonian approximation in general relativity, using the (3+1) formalism. Our formulation coincides…
The non-linear $\Sigma$-Model minimally coupled with Maxwell theory in $3+1$ dimensions possesses a topologically non-trivial sector characterized by ``lasagna''-like configurations. We demonstrate that, when a specific quantization…
Studying quantum field theories through geometric principles has revealed deep connections between physics and mathematics, including the discovery by Cachazo, Early, Guevara and Mizera (CEGM) of a generalization of biadjoint scalar…
We investigate a linearised Calder\'on problem in a two-dimensional bounded simply connected $C^{1,\alpha}$ domain $\Omega$. After extending the linearised problem for $L^2(\Omega)$ perturbations, we orthogonally decompose $L^2(\Omega) =…
We prove to all orders of the loop expansion the low energy theorems of hidden local symmetries in four-dimensional nonlinear sigma models based on the coset space $G/H$, with $G$ and $H$ being arbitrary compact groups. Although the models…
In theories with renormalons the perturbative series is factorially divergent even after restricting to a given order in $1/N$, making the $1/N$ expansion a natural testing ground for the theory of resurgence. We study in detail the…
We discuss the quantized theory of a pure-gauge non-abelian vector field (flat connection) as it would appear in a mass term a` la Stueckelberg. However the paper is limited to the case where only the flat connection is present (no field…
Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled…
This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…
We perform a non-perturbative study of the scale-dependent renormalisation factors of a complete set of dimension-six four-fermion operators. The renormalisation-group (RG) running is determined in the continuum limit for a specific…
Recently it has been claimed that ordinary perturbation theory (OPT) gives incorrect weak coupling expansions for lattice O(N) non-linear sigma models in the infinite volume limit, and in particular that the two-dimensional non-abelian…
The 1+1D O(3) non-linear {\sigma}-model is a model system for future quantum lattice simulations of other asymptotically-free theories, such as non-Abelian gauge theories. We find that utilizing dimensional reduction can make efficient use…
For a theory with first and second class constraints, we propose a procedure for conversion of second class constraints based on deformation the structure of local symmetries of the Lagrangian formulation. It does not require extension or…
As a first application of our renormalisation group approach to non-local matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean two-dimensional noncommutative \phi^4-theory. It is widely believed that this model is…
The short-distance singularity of the product of a composite scalar field that deforms a field theory and an arbitrary composite field can be expressed geometrically by the beta functions, anomalous dimensions, and a connection on the…
Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect we argue that the nonperturbative effect associated with the perturbation theory should have a…
Global symmetries can be generalised to transformations generated by topological operators, including cases in which the topological operator does not have an inverse. A family of such topological operators are intimately related to…
We study two-dimensional ${\cal N}=(2,2)$ gauge theory and its dualized system in terms of complex (linear) superfields and their alternatives. Although this technique itself is not new, we can obtain a new model, the so-called…
We discuss the structure of the non-anticommutative N=2 non-linear sigma-model in two dimensions, constructing differential operators which implement the deformed supersymmetry generators and using them to reproduce the classical action. We…