Wrapped D4-branes from maximal 6D gauged supergravity

We study a large class of domain wall solutions with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>M</a:mi> <a:mi>k</a:mi> <a:msub> <a:mi>w</a:mi> <a:mn>3</a:mn> </a:msub> <a:mo>×</a:mo> <a:msup> <a:mi mathvariant="normal">Σ</a:mi> <a:mn>2</a:mn> </a:msup> </a:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>M</d:mi> <d:mi>k</d:mi> <d:msub> <d:mi>w</d:mi> <d:mn>2</d:mn> </d:msub> <d:mo>×</d:mo> <d:msup> <d:mi mathvariant="normal">Σ</d:mi> <d:mn>3</d:mn> </d:msup> </d:math> slices from maximal gauged supergravity in six dimensions. <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mi mathvariant="normal">Σ</g:mi> <g:mn>2</g:mn> </g:msup> </g:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msup> <j:mi mathvariant="normal">Σ</j:mi> <j:mn>3</j:mn> </j:msup> </j:math> are given by a Riemann surface and a three-manifold with constant curvature while <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>M</m:mi> <m:mi>k</m:mi> <m:msub> <m:mi>w</m:mi> <m:mrow> <m:mn>3</m:mn> <m:mo>,</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msub> </m:math> denotes three-/two-dimensional Minkowski space. We consider the maximal gauged supergravity with <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>C</o:mi> <o:mi>S</o:mi> <o:mi>O</o:mi> <o:mo stretchy="false">(</o:mo> <o:mi>p</o:mi> <o:mo>,</o:mo> <o:mi>q</o:mi> <o:mo>,</o:mo> <o:mn>5</o:mn> <o:mo>−</o:mo> <o:mi>p</o:mi> <o:mo>−</o:mo> <o:mi>q</o:mi> <o:mo stretchy="false">)</o:mo> </o:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>C</s:mi> <s:mi>S</s:mi> <s:mi>O</s:mi> <s:mo stretchy="false">(</s:mo> <s:mi>p</s:mi> <s:mo>,</s:mo> <s:mi>q</s:mi> <s:mo>,</s:mo> <s:mn>4</s:mn> <s:mo>−</s:mo> <s:mi>p</s:mi> <s:mo>−</s:mo> <s:mi>q</s:mi> <s:mo stretchy="false">)</s:mo> <s:mo>⋉</s:mo> <s:msup> <s:mi mathvariant="double-struck">R</s:mi> <s:mn>4</s:mn> </s:msup> </s:math> gauge groups arising from an <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msup> <x:mi>S</x:mi> <x:mn>1</x:mn> </x:msup> </x:math> reduction of seven-dimensional maximal gauged supergravity with <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi>C</z:mi> <z:mi>S</z:mi> <z:mi>O</z:mi> <z:mo stretchy="false">(</z:mo> <z:mi>p</z:mi> <z:mo>,</z:mo> <z:mi>q</z:mi> <z:mo>,</z:mo> <z:mn>5</z:mn> <z:mo>−</z:mo> <z:mi>p</z:mi> <z:mo>−</z:mo> <z:mi>q</z:mi> <z:mo stretchy="false">)</z:mo> </z:math> and <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mi>C</db:mi> <db:mi>S</db:mi> <db:mi>O</db:mi> <db:mo stretchy="false">(</db:mo> <db:mi>p</db:mi> <db:mo>,</db:mo> <db:mi>q</db:mi> <db:mo>,</db:mo> <db:mn>4</db:mn> <db:mo>−</db:mo> <db:mi>p</db:mi> <db:mo>−</db:mo> <db:mi>q</db:mi> <db:mo stretchy="false">)</db:mo> </db:math> gauge groups. The two types of gauge group can be embedded in type IIA theory via consistent truncations on <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:msup> <hb:mi>H</hb:mi> <hb:mrow> <hb:mi>p</hb:mi> <hb:mo>,</hb:mo> <hb:mi>q</hb:mi> </hb:mrow> </hb:msup> <hb:mo>×</hb:mo> <hb:msup> <hb:mi mathvariant="double-struck">R</hb:mi> <hb:mrow> <hb:mn>5</hb:mn> <hb:mo>−</hb:mo> <hb:mi>p</hb:mi> <hb:mo>−</hb:mo> <hb:mi>q</hb:mi> </hb:mrow> </hb:msup> </hb:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:msup> <kb:mi>H</kb:mi> <kb:mrow> <kb:mi>p</kb:mi> <kb:mo>,</kb:mo> <kb:mi>q</kb:mi> </kb:mrow> </kb:msup> <kb:mo>×</kb:mo> <kb:msup> <kb:mi mathvariant="double-struck">R</kb:mi> <kb:mrow> <kb:mn>4</kb:mn> <kb:mo>−</kb:mo> <kb:mi>p</kb:mi> <kb:mo>−</kb:mo> <kb:mi>q</kb:mi> </kb:mrow> </kb:msup> <kb:mo>×</kb:mo> <kb:msup> <kb:mi>S</kb:mi> <kb:mn>1</kb:mn> </kb:msup> </kb:math> , respectively. By performing topological twists on <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"> <nb:msup> <nb:mi mathvariant="normal">Σ</nb:mi> <nb:mn>2</nb:mn> </nb:msup> </nb:math> and <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:msup> <qb:mi mathvariant="normal">Σ</qb:mi> <qb:mn>3</qb:mn> </qb:msup> </qb:math> , we find a number of solutions interpolating between locally flat domain walls in the UV and curved domain walls with <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"> <tb:mi>M</tb:mi> <tb:mi>k</tb:mi> <tb:msub> <tb:mi>w</tb:mi> <tb:mn>3</tb:mn> </tb:msub> <tb:mo>×</tb:mo> <tb:msup> <tb:mi mathvariant="normal">Σ</tb:mi> <tb:mn>2</tb:mn> </tb:msup> </tb:math> and <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"> <wb:mi>M</wb:mi> <wb:mi>k</wb:mi> <wb:msub> <wb:mi>w</wb:mi> <wb:mn>2</wb:mn> </wb:msub> <wb:mo>×</wb:mo> <wb:msup> <wb:mi mathvariant="normal">Σ</wb:mi> <wb:mn>3</wb:mn> </wb:msup> </wb:math>