Identification of perturbative ambiguity canceled against bion

Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb C P^{N-1}$ models

We derive the semiclassical contributions from the real and complex bions in the two-dimensional $\mathbb C P^{N-1}$ sigma model on ${\mathbb R} \times S^{1}$ with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the $\mathbb C P^{N-1}$ quantum mechanics. The bion solutions have …

Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model

This work is a step towards a non-perturbative continuum definition of quantum field theory (QFT), beginning with asymptotically free two dimensional non-linear sigma-models, using recent ideas from mathematics and QFT. The ideas from mathematics are resurgence theory, the trans-series framework, and Borel-Ecalle resummation. The ideas from QFT use continuity on R^1 x S^1_L, i.e, the absence of any phase transition as N \to infinity, or rapid-crossovers for finite-N, and the small-L weak coupling limit to render the semi-classical sector well-defined and calculable. We classify semi-classical …

Infrared renormalon in the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$

In the leading order of the large-$N$ approximation, we study the renormalon ambiguity in the gluon (or, more appropriately, photon) condensate in the 2D supersymmetric $\mathbb{C}P^{N-1}$ model on~$\mathbb{R}\times S^1$ with the $\mathbb{Z}_N$ twisted boundary conditions. In our large~$N$ limit, the combination $ΛR$, where $Λ$ is the dynamical scale and $R$~is the $S^1$ radius, is kept fixed (we set $ΛR\ll1$ so that the perturbative expansion with respect to the coupling constant at the mass scale~$1/R$ is meaningful). We extract the perturbative part from the large-$N$ expression of the gluo…

Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}P^{N-1}$ Models

We discuss the non-perturbative contributions from real and complex saddle point solutions in the $\mathbb{C}P^1$ quantum mechanics with fermionic degrees of freedom, using the Lefschetz thimble formalism beyond the gaussian approximation. We find bion solutions, which correspond to (complexified) instanton-antiinstanton configurations stabilized in the presence of the fermionic degrees of freedom. By computing the one-loop determinants in the bion backgrounds, we obtain the leading order contributions from both the real and complex bion solutions. To incorporate quasi zero modes which become …

Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings

In the previous papers, it is pointed out that a supersymmetric double-well matrix model corresponds to a two-dimensional type IIA superstring theory on a Ramond-Ramond background at the level of correlation functions. This was confirmed by agreement between their planar correlation functions. The supersymmetry in the matrix model corresponds to the target space supersymmetry and it is shown to be spontaneously broken by nonperturbative effect. Furthermore, in the matrix model we computed one-point functions of single-trace operators to all order of genus expansion in its double scaling limit.…

洛伦兹量子宇宙学的复兴：无边界鞍点与隧穿鞍点周围量子引力修正的重整化

Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points

该研究利用Lefschetz thimble分析和复兴理论重新审视宇宙波函数的路径积分方法，解决洛伦兹量子宇宙学中参数空间位于Stokes线导致的结构模糊问题，证明复兴在量子宇宙学中有效。