Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local $${\mathbb{C}\mathbb{P}^2}$$

The holomorphic anomaly equations describe B-model closed topological strings in Calabi–Yau geometries. Having been used to construct perturbative expansions, it was recently shown that they can also be extended past perturbation theory by making use of resurgent transseries. These yield formal nonperturbative solutions, showing integrability of the holomorphic anomaly equations at the nonperturbative level. This paper takes such constructions one step further by working out in great detail the specific example of topological strings in the mirror of the local \({\mathbb{C}\mathbb{P}^2}\) toric Calabi–Yau background, and by addressing the associated (resurgent) large-order analysis of both perturbative and multi-instanton sectors. In particular, analyzing the asymptotic growth of the perturbative free energies, one finds contributions from three different instanton actions related by \({\mathbb{Z}_3}\) symmetry, alongside another action related to the Kähler parameter. Resurgent transseries methods then compute, from the extended holomorphic anomaly equations, higher instanton sectors and it is shown that these precisely control the asymptotic behavior of the perturbative free energies, as dictated by resurgence. The asymptotic large-order growth of the one-instanton sector unveils the presence of resonance, i.e., each instanton action is necessarily joined by its symmetric contribution. The structure of different resurgence relations is extensively checked at the numerical level, both in the holomorphic limit and in the general nonholomorphic case, always showing excellent agreement with transseries data computed out of the nonperturbative holomorphic anomaly equations. The resurgence relations further imply that the string free energy displays an intricate multi-branched Borel structure, and that resonance must be properly taken into account in order to describe the full transseries solution.     

Ambiguities in the up-quark mass

It has long been known that no physical singularity is encountered as up-quark mass is adjusted from small positive to negative values as long as all other quarks remain massive. This is tied to an additive ambiguity in the definition of the quark mass. This calls into question the acceptability of attempts to solve the strong CP problem via a vanishing mass for the lightest quark.     

Nonperturbative solutions of the Lane-Emden equation

A new, iterative approach to solving the Lane-Emden equation leads to approximate solutions which display the coupling constant as a persistent interaction. The approach generalizes to nonlinear field equations.     

Nonperturbative study of the two-frequency sine-Gordon model

The two-frequency sine-Gordon model is examined. The focus is mainly on the case when the ratio of the frequencies is 1/2, given the recent interest in the literature. We discuss the model both in a perturbative (form factor perturbation theory) and a nonperturbative (truncated conformal space approach) framework, and give particular attention to a phase transition conjectured earlier by Delfino and Mussardo. We give substantial evidence that the transition is of second order and that it is in the Ising universality class. Furthermore, we check the UV-IR operator correspondence and conjecture the phase diagram of the theory.     

Ambiguities in the infrared regularization of QCD

The next-to-leading corrections of leading-log asymptotic freedom are determined in the known infrared (IR) regularization schemes. On- and off-shell calculation leads to different answers; the n-dimensional regularization of IR and mass singularities agrees with the on-shell results. The non-log corrections in Drell-Yan processes are important for Q² ? 10³ GeV².     

Nonperturbative parton distributions and the proton spin problem

The Lorentz contracted form of the static wave functions is used to calculate the valence parton distributions for mesons and baryons, boosting the rest frame solutions of the path integral Hamiltonian. It is argued that nonperturbative parton densities are due to excitedmultigluon baryon states. A simplemodel is proposed for these states ensuring realistic behavior of valence and sea quarks and gluon parton densities at Q² = 10 (GeV/c)². Applying the same model to the proton spin problem one obtains Σ₃ = 0.18 for the same Q².     

Nonperturbative QCD near the light cone

We give an overview of current theoretical approaches to nonperturbative QCD. We especially discuss QCD near the light cone.     

Nonperturbative QCD vacuum and colour superconductivity

We discuss the possibility of existence of colour superconducting state in real QCD vacuum with nonzero _sGG. We argue, that nonperturbative gluonic fields might play a crucial role in colour superconductivity scenario.     

Nonperturbative model of Liouville gravity

We formulate nonperturbative 2D gravity in the framework of Liouville theory. In particular, we express the specific heat of pure gravity in terms of an expansion of integrals on moduli spaces of punctured Riemann spheres. We recognize the relevant divisors on moduli spaces and write the integrands in terms of the Liouville action. We evaluate the integrals (rational intersections) and show that satisfies the Painlevé I.     

Nonperturbative heavy-quark diffusion in the quark-gluon plasma

We evaluate heavy-quark (HQ) transport properties in a quark-gluon plasma (QGP) within a Brueckner many-body scheme employing interaction potentials extracted from thermal lattice QCD. The in-medium T matrices for elastic charm- and bottom-quark scattering off light quarks in the QGP are dominated by attractive meson and diquark channels which support resonance states up to temperatures of ~1.5T(c). The resulting drag coefficient increases with decreasing temperature, contrary to expectations based on perturbative QCD scattering. Employing relativistic Langevin simulations we compute HQ spectra and elliptic flow in sqrt[s(NN)]=200 GeV Au-Au collisions. A good agreement with electron decay data supports our nonperturbative computation of HQ diffusion, indicative for a strongly coupled QGP.     

对单胶子交换势的非微扰修正研究

对单胶子交换势的非微扰修正进行了系统研究,结果表明,要获得规范不变的修正形式,QCD真空胶子场必须取为协变规范.在协变规范下,给出了单胶子交换势的非微扰修正的新形式.     

Nonperturbative dynamics in the color-magnetic QCD vacuum

In the deconfinement phase of QCD, quarks and gluons interact with the dense stochastic color-magnetic vacuum. We consider the dynamics of quarks in this deconfinement phase using the field correlators method and derive an effective nonperturbative interquark potential, in addition to the usual perturbative short-range interaction. We find the resulting angular-momentum-dependent interaction to be attractive enough to maintain bound states and, for light quarks (and gluons), to cause emission of quark and gluon pairs. Possible consequences for the strong-interacting quark-gluon plasma are briefly discussed. The text was submitted by the authors in English.     

A Nonperturbative Regularization of the Supersymmetric Schwinger Model

It is shown that noncommutative geometry is a nonperturbative regulator which can manifestly preserve a space supersymmetry and a supergauge symmetry while keeping only finite number of degrees of freedom in the theory. The simplest N= 1 case of the U(1) supergauge theory on the sphere is worked out in detail. Received: 15 March 1999 / Accepted: 8 April 1999     

Nonperturbative results for the spectrum of surface-disordered waveguides

We calculated the spectrum of normal scalar waves in a planar waveguide with absolutely soft randomly rough boundaries. Our approach is beyond perturbation theories in the roughness heights and slopes and is based instead on the exact boundary scattering potential. The spectrum is proved to be a nearly real nonanalytic function of the dispersion zeta(2) of the roughness heights (with square-root singularity) as zeta(2)?0 . The opposite case of large boundary defects is summarized.     

Nonperturbative dressing of nucleons by mesons

Following Feynman's treatment of the polaron problem we present an approximate non-perturbative method of dressing nucleons by scalar and vector mesons: after integrating out the meson fields in the path integral we perform a variational calculation for the effective two-time action of the nucleon by using the same ansatz as Feynman did for the polaron. New features arise from the vector mesons which lead to velocity-dependent terms. We obtain numerical results for the radius and the mean number of the mesons of the dressed particle and derive the effective action in theA nucleon case.