TY - JOUR

T1 - N = 4 superconformal n-particle mechanics via superspace

AU - Krivonos, Sergey

AU - Lechtenfeld, Olaf

AU - Polovnikov, Kirill

N1 - Funding Information: We are indebted to Anton Galajinsky and Anton Sutulin for collaboration at an early stage of this project. S.K. is grateful to A.P. Isaev for discussions. K.P. thanks the ITP at Leibniz Universität Hannover for hospitality and the DAAD and the Dynasty Foundation for support. Funding Information: This work was partially supported by INTAS under contract 05-7928, by an RF Presidential grant NS-2553.2008.2 as well as by the grants RFBR-08-02-90490-Ukr, 06-02-16684, 06-01-00627-a, and DFG 436 Rus 113/669/03. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2009/8/21

Y1 - 2009/8/21

N2 - We revisit the (untwisted) superfield approach to one-dimensional multi-particle systems with N = 4 superconformal invariance. The requirement of a standard (flat) bosonic kinetic energy implies the existence of inertial (super-)coordinates, which is nontrivial beyond three particles. We formulate the corresponding integrability conditions, whose solution directly yields the superpotential, the two prepotentials and the bosonic potential. The structure equations for the two prepotentials, including the WDVV equation, follow automatically. The general solution for translation-invariant three-particle models is presented and illustrated with examples. For the four-particle case, we take advantage of known WDVV solutions to construct a D3 and a B3 model, thus overcoming a previously-found barrier regarding the bosonic potential. The general solution and classification remain a challenge.

AB - We revisit the (untwisted) superfield approach to one-dimensional multi-particle systems with N = 4 superconformal invariance. The requirement of a standard (flat) bosonic kinetic energy implies the existence of inertial (super-)coordinates, which is nontrivial beyond three particles. We formulate the corresponding integrability conditions, whose solution directly yields the superpotential, the two prepotentials and the bosonic potential. The structure equations for the two prepotentials, including the WDVV equation, follow automatically. The general solution for translation-invariant three-particle models is presented and illustrated with examples. For the four-particle case, we take advantage of known WDVV solutions to construct a D3 and a B3 model, thus overcoming a previously-found barrier regarding the bosonic potential. The general solution and classification remain a challenge.

UR - http://www.scopus.com/inward/record.url?scp=65249178381&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2009.03.001

DO - 10.1016/j.nuclphysb.2009.03.001

M3 - Article

AN - SCOPUS:65249178381

VL - 817

SP - 265

EP - 283

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -