In string theory, an important role is played by certain Lie groups which are locally isomorphic to It has long been known that these groups are actually isomorphic not to but rather to the groups for which the half-spin representations are faithful, which we propose to call (They are known in the physics literature by the ambiguous name of “”) Recent work on string duality has shown that the distinction between and can have a definite physical significance. This work is a survey of the relevant properties of and its subgroups.
REFERENCES
1.
L. O’Raifeartaigh, Group Structure of Gauge Theories (Cambridge University Press, Cambridge, 1987).
2.
M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge University Press, Cambridge, 1987).
3.
4.
5.
6.
7.
D. J.
Gross
, J. A.
Harvey
, E.
Martinec
, and R.
Rohm
, Nucl. Phys. B
256
, 253
(1985
).8.
G. G. Ross, Grand Unified Theories (Addison–Wesley, Reading, 1984).
9.
M.
Berkooz
, R. G.
Leigh
, J.
Polchinski
, J. H.
Schwarz
, N.
Seiberg
, and E.
Witten
, Nucl. Phys. B
475
, 115
(1996
).10.
11.
12.
13.
14.
H. B. Lawson and M. L. Michelsohn, Spin Geometry (Princeton University Press, Princeton, 1989).
15.
I. R. Porteous, Clifford Algebras and the Classical Groups (Cambridge University Press, Cambridge, 1995).
16.
T. Bröcker and T. tom Dieck, Representations of Compact Lie Groups (Springer-Verlag, Berlin, 1985).
17.
18.
L.
Alvarez-Gaumé
, P.
Ginsparg
, G.
Moore
, and C.
Vafa
, Phys. Lett. B
171
, 155
(1986
).19.
20.
21.
22.
J. A. Wolf, Spaces of Constant Curvature (Publish or Perish, Wilmington, 1984).
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© 1999 American Institute of Physics.
1999
American Institute of Physics
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