Resurgence and 1/N Expansion in Integrable Field Theories

In theories with renormalons the perturbative series is factorially divergent even after restricting to a given order in 1/N, making the 1/N expansion a natural testing ground for the theory of resurgence. We study in detail the interplay between resurgent properties and the 1/N expansion in various integrable field theories with renormalons. We focus on the free energy in the presence of a chemical potential coupled to a conserved charge, which can be computed exactly with the thermodynamic Bethe ansatz (TBA). In some examples, like the first 1/N correction to the free energy in the non-linear sigma model, the terms in the 1/N expansion can be fully decoded in terms of a resurgent trans-series in the coupling constant. In the principal chiral field we find a new, explicit solution for the large N free energy which can be written as the median resummation of a trans-series with infinitely many, analytically computable IR renormalon corrections. However, in other examples, like the Gross-Neveu model, each term in the 1/N expansion includes non-perturbative corrections which can not be predicted by a resurgent analysis of the corresponding perturbative series. We also study the properties of the series in 1/N. In the Gross-Neveu model, where this is convergent, we analytically continue the series beyond its radius of convergence and show how the continuation matches with known dualities with sine-Gordon theories.

All-dielectric chiral-field-enhanced Raman optical activity

Raman optical activity (ROA) is effective for studying the conformational structure and behavior of chiral molecules in aqueous solutions and is advantageous over X-ray crystallography and nuclear magnetic resonance spectroscopy in sample preparation and cost performance. However, ROA signals are inherently minuscule; 3–5 orders of magnitude weaker than spontaneous Raman scattering due to the weak chiral light–matter interaction. Localized surface plasmon resonance on metallic nanoparticles has been employed to enhance ROA signals, but suffers from detrimental spectral artifacts due to its photothermal heat generation and inability to efficiently transfer and enhance optical chirality from the far field to the near field. Here we demonstrate all-dielectric chiral-field-enhanced ROA by devising a silicon nanodisk array and exploiting its dark mode to overcome these limitations. Specifically, we use it with pairs of chemical and biological enantiomers to show >100x enhanced chiral light–molecule interaction with negligible artifacts for ROA measurements.

An $$ \mathcal{N} $$ = 1 Lagrangian for an $$ \mathcal{N} $$ = 3 SCFT

We propose that a certain 4d$$ \mathcal{N} $$ N = 1 SU(2) × SU(2) gauge theory flows in the IR to an $$ \mathcal{N} $$ N = 3 SCFT plus a single free chiral field. The specific $$ \mathcal{N} $$ N = 3 SCFT has rank 1 and a dimension three Coulomb branch operator. The flow is generically expected to land at the $$ \mathcal{N} $$ N = 3 SCFT deformed by the marginal deformation associated with said Coulomb branch operator. We also present a discussion about the properties expected of various RG invariant quantities from $$ \mathcal{N} $$ N = 3 superconformal symmetry, and use these to test our proposal. Finally, we discuss a generalization to another $$ \mathcal{N} $$ N = 1 model that we propose is related to a certain rank 3 $$ \mathcal{N} $$ N = 3 SCFT through the turning of certain marginal deformations.

Fractional derivative of inverse matrix and its applications to soliton theory

In this paper, a formula of the local fractional partial derivative of inverse matrix is presented and proved. With the help of the derived formula, two new non-linear PDE are derived including the local fractional non-isospectral self-dual Yang-Mills equation and the local fractional principal chiral field equation. It is shown that the formula of the local fractional partial derivative of inverse matrix can be used to derive some other local fractional non-linear PDE in soliton theory.

Linearized electromagnetic and gravito-Heavisidian chirality in split octonion space-time

In this paper, we construct a split octonionic mathematical approach to generalized electromagnetic and gravito-Heavisidian chirality of dyons by modification of the Drude–Born–Fedorov constitutive relations. In this context, we describe dual Euclidean space-times structure associated with [Formula: see text] Zorn’s vector matrix realization of split octonion. As such, using the Zorn’s vector matrix realization, an alternative form of generalized Proca–Maxwell equations of massive dyons is obtained in chiral media. It is well known that in weak unified gravito-Heavisidian field, the Einstein’s equations become Maxwell-like equations under the first approximation. Thus, we study the gravito-Heavisidian analogous theory to electromagnetic theory, and discuss the Drude–Born–Fedorov constitutive relations, gravito-Heavisidian field, Proca–Maxwell equations and gravito-Heavisidian wave equations for linear gravitational chiral field of gravito-dyons in flat split octonion space-time.

Stochastic Lévy differential operators and Yang–Mills equations

The relationship between the Yang–Mills equations and the stochastic analogue of Lévy differential operators is studied. The value of the stochastic Lévy–Laplacian is found by means of Cèsaro averaging of directional derivatives on the stochastic parallel transport. It is shown that the Yang–Mills equations and the Lévy–Laplace equation for such Laplacian are not equivalent in contrast to the deterministic case. An equation equivalent to the Yang–Mills equations is obtained. The equation contains the Lévy divergence. It is proved that the Yang–Mills action functional can be represented as an infinite-dimensional analogue of the Direchlet functional of a chiral field. This analogue is also derived using Cèsaro averaging.