TY - JOUR

T1 - Closed N = 2 strings

T2 - Picture-changing, hidden symmetries and SDG hierarchy

AU - Lechtenfeld, Olaf

AU - Popov, Alexander D.

N1 - Funding Information: A. D. Popov thanks the Institut für Theoretische Physik der Universität Hannover for its hospitality. The work of A. D. Popov was partially supported by the grant RFBR-99-01-01076 and \Freundeskreis der Universität Hannover e.V." O. Lechten-feld acknowledges support by DFG under the grant LE-838/5. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2000/10/20

Y1 - 2000/10/20

N2 - We study the action of picture-changing and spectral flow operators on a ground ring of ghost number zero operators in the chiral BRST cohomology of the closed N = 2 string and describe an infinite set of symmetry charges acting on physical states. The transformations of physical string states are compared with symmetries of self-dual gravity which is the effective field theory of the closed N = 2 string. We derive all infinitesimal symmetries of the self-dual gravity equations in (2+2)-dimensional space-time and introduce an infinite hierarchy of commuting flows on the moduli space of self-dual metrics. The dependence on moduli parameters can be recovered by solving the equations of the SDG hierarchy associated with an infinite set of Abelian symmetries generated recursively from translations. These nonlocal Abelian symmetries are shown to coincide with the hidden Abelian string symmetries responsible for the vanishing of most scattering amplitudes. Therefore, N = 2 string theory 'predicts' not only self-dual gravity but also the SDG hierarchy.

AB - We study the action of picture-changing and spectral flow operators on a ground ring of ghost number zero operators in the chiral BRST cohomology of the closed N = 2 string and describe an infinite set of symmetry charges acting on physical states. The transformations of physical string states are compared with symmetries of self-dual gravity which is the effective field theory of the closed N = 2 string. We derive all infinitesimal symmetries of the self-dual gravity equations in (2+2)-dimensional space-time and introduce an infinite hierarchy of commuting flows on the moduli space of self-dual metrics. The dependence on moduli parameters can be recovered by solving the equations of the SDG hierarchy associated with an infinite set of Abelian symmetries generated recursively from translations. These nonlocal Abelian symmetries are shown to coincide with the hidden Abelian string symmetries responsible for the vanishing of most scattering amplitudes. Therefore, N = 2 string theory 'predicts' not only self-dual gravity but also the SDG hierarchy.

UR - http://www.scopus.com/inward/record.url?scp=0034692969&partnerID=8YFLogxK

U2 - 10.1142/S0217751X00001865

DO - 10.1142/S0217751X00001865

M3 - Article

AN - SCOPUS:0034692969

VL - 15

SP - 4191

EP - 4236

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

SN - 0217-751X

IS - 26

ER -