Some exact results in chiral gauge theories
Csaba Csáki, Hitoshi Murayama, Ofri Telem
Abstract
We analyze dynamics of chiral gauge theories based on the $SU(N)$ gauge group with one antisymmetric tensor $A$ and ($N\ensuremath{-}4$) antifundamentals ${F}_{i}$ when $N$ is odd. Based on the continuity to the supersymmetric gauge theories with anomaly-mediated supersymmetry breaking, we claim that the global $SU(N\ensuremath{-}4)$ symmetry is spontaneously broken to $Sp(N\ensuremath{-}5)$. There are $N\ensuremath{-}5$ massless fermions as a fundamental representation of $Sp(N\ensuremath{-}5)$, and another massless fermion, together saturating the anomaly matching conditions. When $N$ is even, the unbroken flavor symmetry is $Sp(N\ensuremath{-}4)$ while there are no massless fermions. Our result is different from the dynamics suggested by tumbling where the full $SU(N\ensuremath{-}4)$ symmetry is unbroken, but the tumbling picture can be modified via the addition of a second condensate to produce the symmetry breaking pattern predicted from our method.