Related papers: Valley Views: Instantons, Large Order Behaviors, a…
According to Lipatov, the high orders of perturbation theory are determined by saddle-point configurations (instantons) of the corresponding functional integrals. According to t'Hooft, some individual large diagrams, renormalons, are also…
The valley method for computing the total high-energy anomalous cross section $S_{anom}$ is the extension of the optical theorem to the case of instanton-antiinstanton backgrounds. As a toy model for baryon number violation in Electroweak…
Based on the new valley equation, we propose the most plausible method for constructing instanton-like configurations in the theory where the presence of a mass scale prevents the existence of the classical solution with a finite radius. We…
Conventionally, perturbative and non-perturbative calculations are performed independently. In this paper, valleys in the configuration space in quantum mechanics are investigated as a way to treat them in a unified manner. All the known…
In quantum mechanics and quantum field theory perturbation theory generically requires the inclusion of extra contributions non-perturbative in the coupling, such as instantons, to reproduce exact results. We show how full non-perturbative…
We discuss numerical aspects of instantons in two- and three-dimensional $\phi^4$ theories with an internal $O(N)$ symmetry group, the so-called $N$-vector model. Combining asymptotic transseries expansions for large argument with…
We address the nonperturbative structure of topological strings and c=1 matrix models, focusing on understanding the nature of instanton effects alongside with exploring their relation to the large-order behavior of the 1/N expansion. We…
We develop a systematic treatment for the quasi-zero modes, which play an important role in nonabelian gauge theories. It can be used to derive the analytic forms for the constrained instantons in the \ymh theory. This will automatically…
The large $k$ asymptotics (perturbation series) for integrals of the form $\int_{\cal F}\mu e^{i k S}$, where $\mu$ is a smooth top form and $S$ is a smooth function on a manifold ${\cal F}$, both of which are invariant under the action of…
High orders in perturbation theory can be calculated by the Lipatov method. For most field theories, the Lipatov asymptotics has the functional form c a^N \Gamma(N+b) (N is the order of perturbation theory); relative corrections to this…
All five-dimensional non-abelian gauge theories have a $U(1)_I$ global symmetry associated with instantonic particles. We describe an obstruction to coupling $U(1)_I$ to a classical background gauge field that occurs whenever the theory has…
The instanton configuration in the SU(2)-gauge system with a Higgs doublet is constructed by using the new valley method. This method defines the configuration by an extension of the field equation and allows the exact conversion of the…
Instantons and renormalons play important roles at the interface between perturbative and non-perturbative quantum field theory. They are both associated with branch points in the Borel transform of asymptotic series, and as such can be…
Based on the intanton approximation of Skyrmion and recent progresses on the holographic approach, we study baryon properties using Skyrmions generated from holographic instantons. First we employ Atiyah and Manton's early observation to…
I develop a formalism for solving topological field theories explicitly, in the case when the explicit expression of the instantons is known. I solve topological Yang-Mills theory with the $k=1$ Belavin {\sl et al.} instanton and…
We use well-resolved direct numerical simulations of high-Reynolds-number turbulence to study a fundamental statistical property of turbulence -- the asymmetry of velocity increments -- with likely implications on important dynamics. This…
Instanton calculations are demonstrated from a viewpoint of twisted topological field theory. Various properties become manifest such that perturbative corrections are terminated at one-loop, and norm cancellations occur between bosonic and…
Problems related to fermions, unitarity and chiral anomaly in high energy electroweak interactions, are investigated. Particular attention is paid to the correct functional integration over fermion fields in the background of…
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy…
Black hole perturbation theory beyond second order is not well understood because typically one defines the meaning of gauge invariance order by order which is ambiguous. In this series of works we therefore developed a new approach which…