Janus and RG-flow interfaces from 5D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> gauged supergravity

We study five-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>N</a:mi><a:mo>=</a:mo><a:mn>4</a:mn></a:math> gauged supergravity coupled to three vector multiplets with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>S</c:mi><c:mi>O</c:mi><c:mo stretchy="false">(</c:mo><c:mn>2</c:mn><c:msub><c:mo stretchy="false">)</c:mo><c:mi>D</c:mi></c:msub><c:mo>×</c:mo><c:mi>S</c:mi><c:mi>O</c:mi><c:mo stretchy="false">(</c:mo><c:mn>3</c:mn><c:mo stretchy="false">)</c:mo></c:math> gauge group. The gauged supergravity admits two supersymmetric <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>AdS</i:mi><i:mn>5</i:mn></i:msub></i:math> vacua. One of the vacua, at the origin of the scalar manifold <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi mathvariant="double-struck">R</k:mi><k:mo>+</k:mo></k:msup><k:mo>×</k:mo><k:mi>S</k:mi><k:mi>O</k:mi><k:mo stretchy="false">(</k:mo><k:mn>5</k:mn><k:mo>,</k:mo><k:mn>3</k:mn><k:mo stretchy="false">)</k:mo><k:mo>/</k:mo><k:mi>S</k:mi><k:mi>O</k:mi><k:mo stretchy="false">(</k:mo><k:mn>5</k:mn><k:mo stretchy="false">)</k:mo><k:mo>×</k:mo><k:mi>S</k:mi><k:mi>O</k:mi><k:mo stretchy="false">(</k:mo><k:mn>3</k:mn><k:mo stretchy="false">)</k:mo></k:math>, preserves <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>N</t:mi><t:mo>=</t:mo><t:mn>4</t:mn></t:math> supersymmetry and the full <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>S</v:mi><v:mi>O</v:mi><v:mo stretchy="false">(</v:mo><v:mn>2</v:mn><v:msub><v:mo stretchy="false">)</v:mo><v:mi>D</v:mi></v:msub><v:mo>×</v:mo><v:mi>S</v:mi><v:mi>O</v:mi><v:mo stretchy="false">(</v:mo><v:mn>3</v:mn><v:mo stretchy="false">)</v:mo></v:math> gauge symmetry. The second <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msub><bb:mi>AdS</bb:mi><bb:mn>5</bb:mn></bb:msub></bb:math> vacuum is <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>N</db:mi><db:mo>=</db:mo><db:mn>2</db:mn></db:math> supersymmetric and invariant under <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mi>S</fb:mi><fb:mi>O</fb:mi><fb:mo stretchy="false">(</fb:mo><fb:mn>2</fb:mn><fb:msub><fb:mo stretchy="false">)</fb:mo><fb:mrow><fb:mi>diag</fb:mi></fb:mrow></fb:msub></fb:math> which is a diagonal subgroup of <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mi>S</jb:mi><jb:mi>O</jb:mi><jb:mo stretchy="false">(</jb:mo><jb:mn>2</jb:mn><jb:msub><jb:mo stretchy="false">)</jb:mo><jb:mi>D</jb:mi></jb:msub></jb:math> and <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mi>S</nb:mi><nb:mi>O</nb:mi><nb:mo stretchy="false">(</nb:mo><nb:mn>2</nb:mn><nb:mo stretchy="false">)</nb:mo><nb:mo>⊂</nb:mo><nb:mi>S</nb:mi><nb:mi>O</nb:mi><nb:mo stretchy="false">(</nb:mo><nb:mn>3</nb:mn><nb:mo stretchy="false">)</nb:mo></nb:math>. By considering a truncation to <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:mi>S</tb:mi><tb:mi>O</tb:mi><tb:mo stretchy="false">(</tb:mo><tb:mn>2</tb:mn><tb:msub><tb:mo stretchy="false">)</tb:mo><tb:mrow><tb:mi>diag</tb:mi></tb:mrow></tb:msub></tb:math> invariant scalars, we find a class of Janus solutions interpolating among these vacua. These solutions should be holographically dual to conformal interfaces within the dual <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:mi>N</xb:mi><xb:mo>=</xb:mo><xb:mn>1</xb:mn></xb:math> and <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:mi>N</zb:mi><zb:mo>=</zb:mo><zb:mn>2</zb:mn></zb:math> Superconformal Field Theories (SCFTs) in four dimensions. In addition, we also find examples of solutions describing renormalization group-flow interfaces between <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:mi>N</bc:mi><bc:mo>=</bc:mo><bc:mn>1</bc:mn></bc:math> and <dc:math xmlns:dc="http://www.w3.org/1998/Math/MathML" display="inline"><dc:mi>N</dc:mi><dc:mo>=</dc:mo><dc:mn>2</dc:mn></dc:math> Superconformal Field Theories (SCFTs) on each side of the interfaces. All of the solutions could possibly be uplifted to eleven dimensions by a consistent truncation of M-theory on <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"><fc:msub><fc:mi>M</fc:mi><fc:mn>3</fc:mn></fc:msub><fc:mo>×</fc:mo><fc:msup><fc:mi>S</fc:mi><fc:mn>2</fc:mn></fc:msup><fc:mo>×</fc:mo><fc:msup><fc:mi>S</fc:mi><fc:mn>1</fc:mn></fc:msup></fc:math> with a 3-manifold <hc:math xmlns:hc="http://www.w3.org/1998/Math/MathML" display="inline"><hc:msub><hc:mi>M</hc:mi><hc:mn>3</hc:mn></hc:msub></hc:math>.