Curved WDVV equation and supersymmetric mechanics

Abstract

We extend the relation between the Witten-Dijkgraaf-Verlinde-Verlinde equation and N = 4 supersymmetric mechanics to arbitrary curved spaces. The resulting curved WDVV equation is written in terms of the third rank Codazzi tensor. We provide the solutions of the curved WDVV equation for the so(n) symmetric conformally flat metrics. We also explicitly demonstrate how each solution of the flat WDVV equation can be lifted up to the curved WDVV solution on the conformally flat spaces.

Original language	English
Article number	012026
Journal	Journal of Physics: Conference Series
Volume	965
Issue number	1
DOIs	https://doi.org/10.1088/1742-6596/965/1/012026
Publication status	Published - 15 Feb 2018
Event	25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017 - Prague, Czech Republic Duration: 6 Jun 2017 → 10 Jun 2017

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1088/1742-6596/965/1/012026

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title = "Curved WDVV equation and supersymmetric mechanics",

abstract = "We extend the relation between the Witten-Dijkgraaf-Verlinde-Verlinde equation and N = 4 supersymmetric mechanics to arbitrary curved spaces. The resulting curved WDVV equation is written in terms of the third rank Codazzi tensor. We provide the solutions of the curved WDVV equation for the so(n) symmetric conformally flat metrics. We also explicitly demonstrate how each solution of the flat WDVV equation can be lifted up to the curved WDVV solution on the conformally flat spaces.",

author = "N. Kozyrev and S. Krivonos and O. Lechtenfeld and A. Nersessian and A. Sutulin",

year = "2018",

month = feb,

day = "15",

doi = "10.1088/1742-6596/965/1/012026",

language = "English",

volume = "965",

journal = "Journal of Physics: Conference Series",

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note = "25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017 ; Conference date: 06-06-2017 Through 10-06-2017",

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TY - JOUR

T1 - Curved WDVV equation and supersymmetric mechanics

AU - Kozyrev, N.

AU - Krivonos, S.

AU - Lechtenfeld, O.

AU - Nersessian, A.

AU - Sutulin, A.

PY - 2018/2/15

Y1 - 2018/2/15

N2 - We extend the relation between the Witten-Dijkgraaf-Verlinde-Verlinde equation and N = 4 supersymmetric mechanics to arbitrary curved spaces. The resulting curved WDVV equation is written in terms of the third rank Codazzi tensor. We provide the solutions of the curved WDVV equation for the so(n) symmetric conformally flat metrics. We also explicitly demonstrate how each solution of the flat WDVV equation can be lifted up to the curved WDVV solution on the conformally flat spaces.

AB - We extend the relation between the Witten-Dijkgraaf-Verlinde-Verlinde equation and N = 4 supersymmetric mechanics to arbitrary curved spaces. The resulting curved WDVV equation is written in terms of the third rank Codazzi tensor. We provide the solutions of the curved WDVV equation for the so(n) symmetric conformally flat metrics. We also explicitly demonstrate how each solution of the flat WDVV equation can be lifted up to the curved WDVV solution on the conformally flat spaces.

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U2 - 10.1088/1742-6596/965/1/012026

DO - 10.1088/1742-6596/965/1/012026

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AN - SCOPUS:85042934765

VL - 965

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

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IS - 1

M1 - 012026

T2 - 25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017

Y2 - 6 June 2017 through 10 June 2017

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