Dynamics of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>E</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:math> chiral gauge theories

We present exact nonperturbative vacuum solutions to chiral gauge theories based on the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>E</a:mi><a:mn>6</a:mn></a:msub></a:math> gauge group and several matter fermions in the fundamental <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn mathvariant="bold">27</c:mn></c:mrow></c:math>-dimensional representation. They are obtained when supersymmetric versions are perturbed by small supersymmetry breaking by anomaly mediation. The universality classes obtained are very different from what can be conjectured by the tumbling hypothesis. In particular, the case with three <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:mn mathvariant="bold">27</f:mn><f:mi mathvariant="normal">s</f:mi></f:mrow></f:math> may have an unbroken SU(3) symmetry with massless composite fermions in <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:mn mathvariant="bold">10</j:mn></j:mrow></j:math> of SU(3). For this case, we employed numerical techniques to obtain the exact ground state.