We define complex Minkowski superspace in four dimensions as the big cell inside a complex flag supermanifold. The complex conformal supergroup acts naturally on this superflag, allowing us to interpret it as the conformal compactification of complex Minkowski superspace. We then consider real Minkowski superspace as a suitable real form of the complex version. Our methods are group theoretic, based on the real conformal supergroup and its Lie superalgebra.
REFERENCES
1.
Y.
Manin
, Gauge Field Theory and Complex Geometry
(Springer
, Berlin
, 1988
) (original Russian edition in 1984).2.
R.
Penrose
, J. Math. Phys.
8
, 345
(1967
).3.
A.
Ferber
, Nucl. Phys. B
132
, 55
(1978
).4.
M.
Kotrla
and J.
Niederle
, Czech. J. Phys., Sect. B
35
, 602
(1985
).5.
P. S.
Howe
and G. G.
Hartwell
, Class. Quantum Grav.
12
, 1823
(1995
).6.
S.
Ferrara
, J.
Wess
, and B.
Zumino
, Phys. Lett.
51
B, 239
(1974
).7.
R.
D’Auria
, S.
Ferrara
, M. A.
Lledó
, and V. S.
Varadarajan
, J. Geom. Phys.
40
, 101
(2001
).8.
V. S.
Varadarajan
, Supersymmetry for Mathematicians: An Introduction
, Courant Lecture Notes
Vol. 1
(Courant Institute of Mathematical Sciences
, New York
, 2004
).9.
P.
Wess
and B.
Zumino
, Nucl. Phys. B
70
, 39
(1974
).10.
V. K.
Dobrev
and V. B.
Petkova
, Fortschr. Phys.
35
, 537
(1987
).11.
V. G.
Kac
, Adv. Math.
26
, 8
(1977
).12.
P.
Deligne
and J.
Morgan
, in Quantum Fields and Strings. A Course for Mathematicians
(Institute for Advanced Studies
, Princeton
, 1999
), Vol. 1
.13.
L.
Caston
and R.
Fioresi
, Mathematical Foundation of Supersymmetry
(in press).14.
M.
Demazure
and P.
Gabriel
, Introduction to Algebraic Geometry and Algebraic Groups
(North-Holland Mathematical Studies
, Amsterdam
, 1970
).15.
F. A.
Berezin
, in Introduction to Superanalysis
, edited by A. A.
Kirillov
(D. Reidel
, Dordrecht
, 1987
). With an appendix by V. I. Ogievetsky. Translated from the Russian by J. Niederle and R. Kotecký. Translation edited by Dimitri
Leĭtes
.© 2007 American Institute of Physics.
2007
American Institute of Physics
You do not currently have access to this content.
