Isomonodromy aspects of the tt∗equations of cecotti and vafa I. Stokes Data

Martin A. Guest; Alexander R. Its; Chang Shou Lin

doi:10.1093/imrn/rnu250

Isomonodromy aspects of the tt∗equations of cecotti and vafa I. Stokes Data

Martin A. Guest, Alexander R. Its, Chang Shou Lin

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We describe all smooth solutions of the two-function tt∗-Toda equations (a version of the tt∗equations or equations for harmonic maps into SLnR/SOn) in terms of (1) asymptotic data, (2) holomorphic data, and (3) monodromy data, and we compute all of this data explicitly. This allows us, in particular, to find all solutions with integral Stokes data. These include solutions associated to non-linear sigma models (quantum cohomology) or Landau-Ginzburg models (unfoldings of singularities), as conjectured by Cecotti and Vafa in the 1990s.

Original language	English
Pages (from-to)	11745-11784
Number of pages	40
Journal	International Mathematics Research Notices
Volume	2015
Issue number	22
DOIs	https://doi.org/10.1093/imrn/rnu250
Publication status	Published - 2015

ASJC Scopus subject areas

Mathematics(all)

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10.1093/imrn/rnu250

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title = "Isomonodromy aspects of the tt∗equations of cecotti and vafa I. Stokes Data",

abstract = "We describe all smooth solutions of the two-function tt∗-Toda equations (a version of the tt∗equations or equations for harmonic maps into SLnR/SOn) in terms of (1) asymptotic data, (2) holomorphic data, and (3) monodromy data, and we compute all of this data explicitly. This allows us, in particular, to find all solutions with integral Stokes data. These include solutions associated to non-linear sigma models (quantum cohomology) or Landau-Ginzburg models (unfoldings of singularities), as conjectured by Cecotti and Vafa in the 1990s.",

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AU - Guest, Martin A.

AU - Its, Alexander R.

AU - Lin, Chang Shou

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N2 - We describe all smooth solutions of the two-function tt∗-Toda equations (a version of the tt∗equations or equations for harmonic maps into SLnR/SOn) in terms of (1) asymptotic data, (2) holomorphic data, and (3) monodromy data, and we compute all of this data explicitly. This allows us, in particular, to find all solutions with integral Stokes data. These include solutions associated to non-linear sigma models (quantum cohomology) or Landau-Ginzburg models (unfoldings of singularities), as conjectured by Cecotti and Vafa in the 1990s.

AB - We describe all smooth solutions of the two-function tt∗-Toda equations (a version of the tt∗equations or equations for harmonic maps into SLnR/SOn) in terms of (1) asymptotic data, (2) holomorphic data, and (3) monodromy data, and we compute all of this data explicitly. This allows us, in particular, to find all solutions with integral Stokes data. These include solutions associated to non-linear sigma models (quantum cohomology) or Landau-Ginzburg models (unfoldings of singularities), as conjectured by Cecotti and Vafa in the 1990s.

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