Living on the walls of super-QCD
Abstract
We study BPS domain walls in four-dimensional N=1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> massive SQCD with gauge group SU(N) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>U</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mi>N</mml:mi> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> and F<N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo><</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> flavors. We propose a class of three-dimensional Chern-Simons-matter theories to describe the effective dynamics on the walls. Our proposal passes several checks, including the exact matching between its vacua and the solutions to the four-dimensional BPS domain wall equations, that we solve in the small mass regime. As the flavor mass is varied, domain walls undergo a second-order phase transition, where multiple vacua coalesce into a single one. For special values of the parameters, the phase transition exhibits supersymmetry enhancement. Our proposal includes and extends previous results in the literature, providing a complete picture of BPS domain walls for F<N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo><</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> massive SQCD. A similar picture holds also for SQCD with gauge group Sp(N) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>p</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mi>N</mml:mi> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> and F < N+1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo><</mml:mo> <mml:mi>N</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> flavors.