Mirror symmetry

About: Mirror symmetry is a research topic. Over the lifetime, 2422 publications have been published within this topic receiving 90786 citations.

Arithmetic mirror symmetry for genus 1 curves with $n$ marked points

Abstract: We establish a $\mathbb{Z}[[t_1,\ldots, t_n]]$-linear derived equivalence between the relative Fukaya category of the 2-torus with $n$ distinct marked points and the derived category of perfect complexes on the $n$-Tate curve. Specialising to $t_1= \ldots =t_n=0$ gives a $\mathbb{Z}$-linear derived equivalence between the Fukaya category of the $n$-punctured torus and the derived category of perfect complexes on the standard (Neron) $n$-gon. We prove that this equivalence extends to a $\mathbb{Z}$-linear derived equivalence between the wrapped Fukaya category of the $n$-punctured torus and the derived category of coherent sheaves on the standard $n$-gon.

Superconformal algebras for twisted connected sums and G2 mirror symmetry

Abstract: We realise the Shatashvili-Vafa superconformal algebra for G2 string compactifications by combining Odake and free conformal algebras following closely the recent mathematical construction of twisted connected sum G2 holonomy manifolds. By considering automorphisms of this realisation, we identify stringy analogues of two mirror maps proposed by Braun and Del Zotto for these manifolds.

The Eynard–Orantin recursion and equivariant mirror symmetry for the projective line

Abstract: We study the equivariantly perturbed mirror Landau–Ginzburg model of ℙ1. We show that the Eynard–Orantin recursion on this model encodes all-genus, all-descendants equivariant Gromov–Witten invariants of ℙ1. The nonequivariant limit of this result is the Norbury–Scott conjecture, while by taking large radius limit we recover the Bouchard–Marino conjecture on simple Hurwitz numbers.

From Infinity to Four Dimensions: Higher Residue Pairings and Feynman Integrals

Abstract: We study a surprising phenomenon in which Feynman integrals in $D=4-2\varepsilon$ space-time dimensions as $\varepsilon \to 0$ can be fully characterized by their behavior in the opposite limit, $\varepsilon \to \infty$. More concretely, we consider vector bundles of Feynman integrals over kinematic spaces, whose connections have a polynomial dependence on $\varepsilon$ and are known to be governed by intersection numbers of twisted forms. They give rise to differential equations that can be obtained exactly as a truncating expansion in either $\varepsilon$ or $1/\varepsilon$. We use the latter for explicit computations, which are performed by expanding intersection numbers in terms of Saito's higher residue pairings (previously used in the context of topological Landau-Ginzburg models and mirror symmetry). These pairings localize on critical points of a certain Morse function, which correspond to regions in the loop-momentum space that were previously thought to govern only the large-$D$ physics. The results of this work leverage recent understanding of an analogous situation for moduli spaces of curves, where the $\alpha' \to 0$ and $\alpha' \to \infty$ limits of intersection numbers coincide for scattering amplitudes of massless quantum field theories.

Mirror symmetry breaking through an internal degree of freedom leading to directional motion.

Abstract: We analyze here the minimal conditions for directional motion (net flow in phase space) of a molecular motor placed on a mirror-symmetric environment and driven by a center-symmetric and time-periodic force field. The complete characterization of the deterministic limit of the dissipative dynamics of several realizations of this minimal model reveals a complex structure in the phase diagram in parameter space, with intertwined regions of pinning (closed orbits) and directional motion. This demonstrates that the mirror symmetry breaking, which is needed for directional motion to occur, can operate through an internal degree of freedom coupled to the translational one.