Tuesday, October 30, 2012

1207.6547 (Richard DeJonghe et al.)

Bott Periodicity and Realizations of Chiral Symmetry in Arbitrary
Dimensions
   [PDF]

Richard DeJonghe, Kimberly Frey, Tom Imbo
We compute the chiral symmetries of the Lagrangian for confining "vector-like" gauge theories with massless fermions in $d$-dimensional Minkowski space and, under a few reasonable assumptions, determine the form of the quadratic fermion condensates which arise through spontaneous breaking of these symmetries. We find that for each type (complex, real, or pseudoreal) of representation of the gauge group carried by the fermions, the chiral symmetries of the Lagrangian, as well as the residual symmetries after dynamical breaking, exactly follow the pattern of Bott periodicity as the dimension changes. The consequences of this for the topological features of the low-energy effective theory are considered.
View original: http://arxiv.org/abs/1207.6547

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