Related papers: Three-loop Correction to the Instanton Density. II…
We present analytic forms of three-loop four-gluon planar amplitudes in pure Yang-Mills theory in this letter. Gauge invariant bases and a set of proper master integrals are chosen such that the amplitudes are explicitly invariant under…
We compactify four-dimensional N=1 gauged supergravity theories on a circle including fluxes for shift-symmetric scalars. Four-dimensional Taub-NUT gravitational instantons universally correct the three-dimensional superpotential in the…
We compute the three-loop corrections to the potential of two heavy quarks. In particular we consider in this Letter the purely gluonic contribution which provides in combination with the fermion corrections of Ref. \cite{Smirnov:2008pn}…
We compute the three-loop four-gluon scattering amplitude in maximally supersymmetric Yang-Mills theory, including its full color dependence. Our result is the first complete computation of a non-planar four-particle scattering amplitude to…
Recent works have explored how scattering amplitudes in quantum self-dual Yang-Mills theory and self-dual gravity can be interpreted as resulting from an anomaly, as first proposed by W. Bardeen. We study this problem in the…
Within the framework of the instanton approach we present analytical results for the following model problems: (i) particle penetration through a parabolic potential barrier, where the instanton solution practically coincides with the exact…
We present a novel method for precise numerical solution of the irreducible two-body problem and apply it to excitons in solids. The approach is based on the Monte Carlo simulation of the two-body Green function specified by Feynman's…
In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton…
Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…
Within the sine-Gordon formalism of a two-dimensional neutral classical Coulomb gas, a convergent expansion with non-perturbative nature is performed to calculate the thermodynamic potential and construct the phase diagram. It is shown that…
Coupled instantons are introduced by generalizing the double well potential to multiple mutually coupled wells. Physically this corresponds to the simultaneous tunneling of multiple degrees of freedom. A system with four equal minima is…
For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the epsilon-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the epsilon-expansion…
We review and elaborate on certain aspects of the connections between instanton counting in maximally supersymmetric gauge theories and the computation of enumerative invariants of smooth varieties. We study in detail three instances of…
We highlight the latest developments in computing higher-order scattering amplitudes with massive internal propagators. The contributing Feynman integrals often lead to special classes of functions, for example, functions associated with…
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…
We present the full two-loop four-graviton amplitudes in N=4,5,6 supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The…
N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop…
We study the influence of quantum fluctuations on the macroscopic quantum tunneling and self-trapping of a two-component Bose-Einstein condensate in a double-well trap. Quantum fluctuations are described by the Lee-Huang-Yang term in the…
We comment on the status of "Steinmann-like" constraints, i.e. all-loop constraints on consecutive entries of the symbol of scattering amplitudes and Feynman integrals in planar ${\cal N}=4$ super-Yang-Mills, which have been crucial for the…
In this paper, we study the three-dimensional noncommutative Maxwell-Chern-Simons theory. In the present analysis, a complete account for the gauge field two-point function renormalizability is presented and physical significant quantities…