Holography of linear dilaton spacetimes from the bottom up

Abstract

The linear dilaton (LD) background is the keystone of a string-derived holographic correspondence beyond <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>AdS</a:mi></a:mrow><a:mrow><a:mi>d</a:mi><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:msub><a:mo>/</a:mo><a:msub><a:mrow><a:mi>CFT</a:mi></a:mrow><a:mrow><a:mi>d</a:mi></a:mrow></a:msub></a:mrow></a:math>. This motivates an exploration of the (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>d</c:mi><c:mo>+</c:mo><c:mn>1</c:mn></c:mrow></c:math>)-dimensional linear dilaton spacetime (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msub><e:mrow><e:mi>LD</e:mi></e:mrow><e:mrow><e:mi>d</e:mi><e:mo>+</e:mo><e:mn>1</e:mn></e:mrow></e:msub></e:mrow></e:math>) and its holographic properties from the low-energy viewpoint. We first notice that the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msub><g:mrow><g:mi>LD</g:mi></g:mrow><g:mrow><g:mi>d</g:mi><g:mo>+</g:mo><g:mn>1</g:mn></g:mrow></g:msub></g:mrow></g:math> space has simple conformal symmetries, that we use to shape an effective field theory (EFT) on the LD background. We then place a brane in the background to study holography at the level of quantum fields and gravity. We find that the holographic correlators from the EFT feature a pattern of singularities at certain kinematic thresholds. We argue that such singularities can be used to bootstrap the putative <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>d</i:mi></i:math>-dimensional dual theory using techniques analogous to those of the cosmological bootstrap program. Turning on finite temperature, we study the holographic fluid emerging on the brane in the presence of a bulk black hole. We find that the holographic fluid is pressureless for any <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>d</k:mi></k:math> due to a cancellation between Weyl curvature and dilaton stress tensor, and verify consistency with the time evolution of the theory. From the fluid thermodynamics, we find a universal temperature and Hagedorn behavior for any <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>d</m:mi></m:math>. This matches the properties of a <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:msub><o:mrow><o:mi>CFT</o:mi></o:mrow><o:mrow><o:mn>2</o:mn></o:mrow></o:msub></o:mrow></o:math> with large <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>T</q:mi><q:mover accent="true"><q:mi>T</q:mi><q:mo stretchy="false">¯</q:mo></q:mover></q:math> deformation, and of little string theory for <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>d</u:mi><u:mo>=</u:mo><u:mn>6</u:mn></u:math>. We also find that the holographic fluid entropy exactly matches the bulk black hole Bekenstein-Hawking entropy. Both the fluid equation of state and the spectrum of quantum fluctuations suggest that the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>d</w:mi></w:math>-dimensional dual theory arising from <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mrow><y:msub><y:mrow><y:mi>LD</y:mi></y:mrow><y:mrow><y:mi>d</y:mi><y:mo>+</y:mo><y:mn>1</y:mn></y:mrow></y:msub></y:mrow></y:math> is generically gapped. Published by the American Physical Society 2024

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