χSB of cascading gauge theory in de Sitter
Alex Buchel
Abstract
A bstract $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 supersymmetric SU( N ) × SU( N + M ) cascading gauge theory of Klebanov et al. [ 1, 2] spontaneously breaks chiral symmetry in Minkowski space-time. We demonstrate that in de Sitter space-time the chiral symmetry breaking occurs for the values of the Hubble constant $$ H\underset{\sim }{<}0.7\Lambda, $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> <mml:munder> <mml:mo><</mml:mo> <mml:mo>~</mml:mo> </mml:munder> <mml:mn>0.7</mml:mn> <mml:mi>Λ</mml:mi> <mml:mo>,</mml:mo> </mml:math> as well as in the narrow window 0.92(1)Λ ≤ H ≤ 0.92(5)Λ. We give a precise definition of the strong coupling scale A of the cascading gauge theory, which is related to the glueball mass scale in the theory m glueball and the asymptotic string coupling g s as $$ \Lambda \sim {g}_s^{1/2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> <mml:mo>~</mml:mo> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mi>s</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> m gluebal.l