Related papers: Field-Theory Amplitudes as Resurgent Functions
In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function…
The renormalization-scheme and scale dependence of the truncated QCD perturbative expansions is one of the main sources of theoretical error of the standard model predictions, especially at intermediate energies. Recently, a class of…
Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients…
Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the…
We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional scalar theories. It is based on 1/N-expansion and results in a logarithmically divergent perturbation theory in…
The mathematical idea of resurgence allows one to obtain nonperturbative information from the large-order behavior of perturbative expansions. This idea can be very fruitful in physics applications, in particular if one does not have access…
Calculations of high multiplicity Higgs amplitudes exhibit a rapid growth that may signal an end of perturbative behavior or even the need for new physics phenomena. As a step towards this problem we consider the quantum mechanical…
We investigate the resurgence structure in quantum mechanical models originating in 2d non-linear sigma models with emphasis on nearly supersymmetric and quasi-exactly solvable parameter regimes. By expanding the ground state energy in…
This text is about the mathematical use of certain divergent power series. The first part is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the…
We extend and apply a recently introduced quasi-particle functional renormalisation group scheme to the two-dimensional Hubbard model with next-nearest-neighbour hopping and away from half filling. We confirm the generation of…
The Nekrasov-Shatashvili limit for the low-energy behavior of N=2 and N=2* supersymmetric SU(2) gauge theories is encoded in the spectrum of the Mathieu and Lam'e equations, respectively. This correspondence is usually expressed via an…
We study a systematic improvement of perturbation theory for gauge fields on the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method,…
With the advancement of strategies for the precision physics programs for the HL-LHC, FCC-ee, FCC-hh, ILC, CLIC, CEPC, and CPPC, the need for proper control of the attendant theoretical precision tags is manifest. We discuss the role that…
The subject of the first section-lecture is concerned with the strength and the weakness of the perturbation theory (PT) approach, that is expansion in powers of a small parameter $\alpha$, in Quantum Theory. We start with outlining a…
The $n$-point amplitudes of gauge and gravity theory are given as a series in the coupling. The recursive derivative expansion is used to find all of the coupling coefficients. Initial conditions to any bare Lagrangian, or of an improved…
We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, renormalization scheme dependence of the scattering amplitude can only…
In effective field theories, the concept of renormalization of perturbative divergences is replaced by renormalization group concepts such as relevance and universality. Universality is related to cutoff scheme independence in…
In general, perturbative expansions of observables in powers of the coupling constant in quantum field theories are asymptotic series. In many cases it is possible to apply resummation techniques to assign a unique finite value to an…
Modular graph functions arise in the calculation of the low-energy expansion of closed-string scattering amplitudes. For toroidal world-sheets, they are ${\rm SL}(2,\mathbb{Z})$-invariant functions of the torus complex structure that have…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…