Related papers: Resurgence theory, ghost-instantons, and analytic …
We introduce and analyze a new quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of…
Numerical Stochastic Perturbation Theory (NSPT) has over the years proved to be a valuable tool, in particular being able to reach unprecedented orders for Lattice Gauge Theories, whose perturbative expansions are notoriously cumbersome.…
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach…
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…
We investigate the ground-state energy of the integrable two dimensional $O(3)$ sigma model in a magnetic field. By determining a large number of perturbative coefficients we explore the closest singularities of the corresponding Borel…
We study the leading nonperturbative corrections to the strong-coupling (ungapped) phase of the Gross-Witten-Wadia (GWW) integral over unitary matrices, to one-loop order. We compute these corrections directly in terms of eigenvalue…
We study the tunneling of virtual matter-antimatter pairs from the quantum vacuum in the presence of a spatially uniform, time-dependent electric background composed of a strong, slow field superimposed with a weak, rapid field. After…
We show that compatibility of supersymmetry with exact semi-classics demands that in calculating multi-instanton amplitudes, the "separation" quasi-zeromode must be complexified and the integration cycles must be found by using complex…
We compute, from first principles, the quantum fluctuations about instanton saddle points of the Euclidean path integral for Einstein gravity coupled to a scalar field. The Euclidean two-point correlator is analytically continued into the…
This is a brief summary of our studies of quantum field theories in a special limit in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the corresponding…
We analyze vacuum tunneling in quantum field theory in a general formalism by using the Wigner representation. In the standard instanton formalism, one usually approximates the initial false vacuum state by an eigenstate of the field…
Direct numerical evaluation of the real-time path integral has a well-known sign problem that makes convergence exponentially slow. One promising remedy is to use Picard-Lefschetz theory to flow the domain of the field variables into the…
Path-integral approach in imaginary and complex time has been proven successful in treating the tunneling phenomena in quantum mechanics and quantum field theories. Latest developments in this field, the proper valley method in imaginary…
Tachyon condensation in quantum field theory (QFT) plays a central role in models of fundamental interactions and cosmology. Inspired by tower truncation in string field theory, ultraviolet completions were proposed with infinite-derivative…
The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study,…
Theories with curvature squared terms in the action are known to contain ghost modes in general. However, if we regard curvature squared terms as quantum corrections to the original theory, the emergence of ghosts may be simply due to the…
The connection between ghost-free formulations of RG-invariant perturbation theory in the both Euclidean and Minkowskian regions is studied. Our basic tool is the "double spectral representation", similar to definition of Adler function,…
A gravitational instanton is found that can tunnel into a new more stable vacuum phase where diffeomorphism invariance is broken and pitchfork bifurcations develop. This tunnelling process involves a double sphaleron-like transition which…
In these lectures I present a review of non-perturbative instanton effects in quantum theories, with a focus on large N gauge theories and matrix models. I first consider the structure of these effects in the case of ordinary differential…
In this work, we present a recurrence relation for the instanton partition function of the $\mathcal{N}=2$ SYM $SU(N)$ gauge theory with $2N$ fundamental multiplets. The main difficulty lies in determining the asymptotic behaviour of the…