相关论文: Some tt* structures and their integral Stokes data

We describe all smooth solutions of the two-function tt*-Toda equations (a version of the tt* equations, or equations for harmonic maps into SL(n,R)/SO(n)) in terms of (i) asymptotic data, (ii) holomorphic data, and (iii) monodromy data.…

In Part I (arXiv:1209.2045) we computed the Stokes data, though not the "connection matrix", for the smooth solutions of the tt*-Toda equations whose existence we established by p.d.e. methods. Here we give an alternative proof of the…

This paper, the third in a series, completes our description of all (radial) solutions on C* of the tt*-Toda equations, using a combination of methods from p.d.e., isomonodromic deformations (Riemann-Hilbert method), and loop groups. We…

We propose a Lie-theoretic definition of the tt*-Toda equations for any complex simple Lie algebra $\mathfrak{g}$, based on the concept of topological-antitopological fusion which was introduced by Cecotti and Vafa. Our main result concerns…

In previous articles we have studied the A_n tt*-Toda equations (topological-antitopological fusion equations of Toda type) of Cecotti and Vafa, giving details mainly for n=3. Here we give a proof of the existence and uniqueness of global…

We give a Lie-theoretic explanation for the convex polytope which parametrizes the globally smooth solutions of the topological-antitopological fusion equations of Toda type (tt$^*$-Toda equations) which were introduced by Cecotti and Vafa.…

Using nonlinear pde techniques, we construct a new family of globally smooth tt* structures. This includes tt* structures associated to the (orbifold) quantum cohomology of a finite number of complex projective spaces and weighted…

Cecotti and Vafa introduced the topological anti-topological fusion (tt*)-equation, whose solutions describe massive deformations of supersymmetric conformal field theories. We provide a rigorous analytic formulation of the $ADE$…

We suggest an explanation for the part of the Satake Correspondence which relates the quantum cohomology of complex Grassmannians and the quantum cohomology of complex projective space, as well as their respective Stokes data, based on the…

We relate the quantum cohomology of minuscule flag manifolds to the tt*-Toda equations, a special case of the topological-antitopological fusion equations which were introduced by Cecotti and Vafa in their study of supersymmetric quantum…

Algebraic holonomic $\mathcal{D}$-modules on a complex line are classified by the associated topological data consisting of local systems with Stokes structure and the nearby and vanishing cycles at the singularities. The Fourier transform…

The classical Stokes matrices for the quantum differential equation of projective n-space are computed, using multisummation and the so-called monodromy identity. Thus, we recover the results of D. Guzzetti that confirm Dubrovin's…

The tt*-equation (topological-anti-topological fusion equation) was introduced by S. Cecotti and C. Vafa for describing massive deformation of supersymmetric conformal field theories. B. Dubrovin formulated the tt*-equation as a flat…

Cecotti and Vafa introduced the tt*-equation (topological-antitopological fusion equation), whose solutions describe massive deformations of supersymmetric conformal field theories. We describe some solutions of the tt*-equation constructed…

An important special class of the tt* equations are the tt*-Toda equations. Guest et al. have given comprehensive studies on the tt*-Toda equations in a series of papers. The fine asymptotics for a large class of solutions of a special…

We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the Cauchy data are holomorphic on the complex…

Multisummation provides a transparent description of Stokes matrices which is reviewed here together with some applications. Examples of moduli spaces for Stokes matrices are computed and discussed. A moduli space for a third Painlev\'e…

For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the…

We observe a general structure theorem for quantum cohomology rings, a non-homogeneous version of the usual cohomology ring encoding information about (almost holomorphic) rational curves. An application is the rigorous computation of the…

We consider the Stokes phenomenon for the solutions of some partial differential equations with variable coefficients in two complex variables, where initial data are holomorphic. We use the theory of (moment) summability and the theory of…