Stability of baryonic black membranes

Near-extremal black membranes with topological (baryonic) <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:msub> <a:mo stretchy="false">)</a:mo> <a:mi>B</a:mi> </a:msub> </a:math> charge of M theory compactified on the coset space <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>M</e:mi> <e:mrow> <e:mn>1</e:mn> <e:mo>,</e:mo> <e:mn>1</e:mn> <e:mo>,</e:mo> <e:mn>0</e:mn> </e:mrow> </e:msup> </e:math> are stable. <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mi>M</g:mi> <g:mrow> <g:mn>1</g:mn> <g:mo>,</g:mo> <g:mn>1</g:mn> <g:mo>,</g:mo> <g:mn>0</g:mn> </g:mrow> </g:msup> </g:math> coset is a <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi mathvariant="double-struck">Z</i:mi> <i:mn>2</i:mn> </i:msub> </i:math> -invariant truncation of a larger <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:msup> <l:mi>Q</l:mi> <l:mrow> <l:mn>1</l:mn> <l:mo>,</l:mo> <l:mn>1</l:mn> <l:mo>,</l:mo> <l:mn>1</l:mn> </l:mrow> </l:msup> </l:math> coset, with diagonal <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>U</n:mi> <n:mo stretchy="false">(</n:mo> <n:mn>1</n:mn> <n:msub> <n:mo stretchy="false">)</n:mo> <n:mi>B</n:mi> </n:msub> <n:mo>≡</n:mo> <n:mi>U</n:mi> <n:mo stretchy="false">(</n:mo> <n:mn>1</n:mn> <n:msub> <n:mo stretchy="false">)</n:mo> <n:mrow> <n:mi>B</n:mi> <n:mo>,</n:mo> <n:mo>+</n:mo> </n:mrow> </n:msub> <n:mo>⊂</n:mo> <n:mi>U</n:mi> <n:mo stretchy="false">(</n:mo> <n:mn>1</n:mn> <n:msubsup> <n:mo stretchy="false">)</n:mo> <n:mi>B</n:mi> <n:mn>2</n:mn> </n:msubsup> </n:math> symmetry of the latter. We show that the baryonic black membranes of M-theory <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:msup> <v:mi>M</v:mi> <v:mrow> <v:mn>1</v:mn> <v:mo>,</v:mo> <v:mn>1</v:mn> <v:mo>,</v:mo> <v:mn>0</v:mn> </v:mrow> </v:msup> </v:math> compactifications are unstable to <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi mathvariant="double-struck">Z</x:mi> <x:mn>2</x:mn> </x:msub> </x:math> -odd gravitational bulk gauge and scalar fluctuations, but only if this bulk scalar is identified with the holographically dual <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mn>2</ab:mn> <ab:mo>+</ab:mo> <ab:mn>1</ab:mn> </ab:math> -dimensional superconformal gauge theory operator of conformal dimension <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi mathvariant="normal">Δ</cb:mi> <cb:mo>=</cb:mo> <cb:mn>1</cb:mn> </cb:math> . The instability is associated with the unstable charge transport of the off-diagonal <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mi>U</fb:mi> <fb:mo stretchy="false">(</fb:mo> <fb:mn>1</fb:mn> <fb:msub> <fb:mo stretchy="false">)</fb:mo> <fb:mrow> <fb:mi>B</fb:mi> <fb:mo>,</fb:mo> <fb:mo>−</fb:mo> </fb:mrow> </fb:msub> <fb:mo>⊂</fb:mo> <fb:mi>U</fb:mi> <fb:mo stretchy="false">(</fb:mo> <fb:mn>1</fb:mn> <fb:msubsup> <fb:mo stretchy="false">)</fb:mo> <fb:mi>B</fb:mi> <fb:mn>2</fb:mn> </fb:msubsup> </fb:math> symmetry.