Teruaki Inagaki and Hiroshi Suzuki JHEP07(2004)038 doi:10.1088/1126-6708/2004/07/038
Teruaki Inagaki1 and Hiroshi Suzuki2
Show affiliationsIn various dimensional euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1+8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factrized form of the Dirac determinant. Similarly, in 2+8n dimensions, there is a difficulty to decompose a classical lattice action of the Weyl fermion into a system of the Majorana-Weyl fermion and thus to obtain a factrized form of the Weyl determinant. Prescriptions based on the overlap formalism do not remove these difficulties. We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in 8n dimensions. For this reason (besides other well-known reasons), a lattice formulation of the N = 1 super Yang-Mills theory in these dimensions is expected to be extremely difficult to find.
Anomalies in Field and String Theories
E-print Number: hep-lat/0406026
Cited: by |
Refers: to
11.10.Kk Field theories in dimensions other than four
11.30.Er Charge conjugation, parity, time reversal, and other discrete symmetries
Issue 07 (July 2004)
Received 17 June 2004, accepted for publication 16 July 2004
Published 11 August 2004
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