SO(4) gauged O(5) Skyrmion on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi mathvariant="normal">R</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math>

We have studied an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>O</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>4</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> gauged <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>O</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>5</e:mn> <e:mo stretchy="false">)</e:mo> </e:math> Skyrmion on <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:msup> <i:mrow> <i:mi mathvariant="normal">I</i:mi> <i:mspace depth="0.0ex" height="0.0ex" width="-0.2em"/> <i:mi mathvariant="normal">R</i:mi> </i:mrow> <i:mrow> <i:mn>4</i:mn> </i:mrow> </i:msup> </i:mrow> </i:math> , which can be seen as a static soliton in <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mn>4</p:mn> <p:mo>+</p:mo> <p:mn>1</p:mn> </p:math> dimensions. This is a sequel of the known <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>S</r:mi> <r:mi>O</r:mi> <r:mo stretchy="false">(</r:mo> <r:mi>D</r:mi> <r:mo stretchy="false">)</r:mo> </r:math> gauged <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mi>O</v:mi> <v:mo stretchy="false">(</v:mo> <v:mi>D</v:mi> <v:mo>+</v:mo> <v:mn>1</v:mn> <v:mo stretchy="false">)</v:mo> </v:math> Skyrmions on <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mrow> <z:msup> <z:mrow> <z:mi mathvariant="normal">I</z:mi> <z:mspace depth="0.0ex" height="0.0ex" width="-0.2em"/> <z:mi mathvariant="normal">R</z:mi> </z:mrow> <z:mrow> <z:mi>D</z:mi> </z:mrow> </z:msup> </z:mrow> </z:math> in <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>D</gb:mi> <gb:mo>=</gb:mo> <gb:mn>2</gb:mn> </gb:math> and in <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>D</ib:mi> <ib:mo>=</ib:mo> <ib:mn>3</ib:mn> </ib:math> , which are likewise localized to an absolute scale and topologically stable, their energies being bounded below by the winding number. In the absence of an analytic proof of existence, some such solutions are constructed numerically. Two families of solutions are found, of which only one possesses a gauge decoupling limit. The curvatures of both of these solutions decay as <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:msup> <kb:mi>r</kb:mi> <kb:mrow> <kb:mo>−</kb:mo> <kb:mn>3</kb:mn> </kb:mrow> </kb:msup> </kb:math> , a property they share with the Yang-Mills instantons on <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mrow> <mb:msup> <mb:mrow> <mb:mi mathvariant="normal">I</mb:mi> <mb:mspace depth="0.0ex" height="0.0ex" width="-0.2em"/> <mb:mi mathvariant="normal">R</mb:mi> </mb:mrow> <mb:mrow> <mb:mn>4</mb:mn> </mb:mrow> </mb:msup> </mb:mrow> </mb:math> .