Universal IR holography, scalar fluctuations, and glueball spectra

We show that the d’Alembertian operator with a possible mass term in the anti–de Sitter (AdS) soliton and more general confining gravity dual backgrounds admits infinitely many different spectra. These can be interpreted as different theories in the infrared and correspond to multitrace deformations of either the Dirichlet or the Neumann theory. We prove that all these fluctuations are normalizable and provide examples of their spectra. Therefore, the AdS soliton can be interpreted as giving a holographic Renormalization Group flow between a universal UV theory at the AdS boundary and these infinitely many possibilities in the IR, obtained by deformations. The massive spectrum of the double trace deformation in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>AdS</a:mi><a:mn>5</a:mn></a:msub></a:math> allows the matching of the large-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>N</c:mi></c:math> glueball masses of lattice <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>QCD</e:mi><e:mn>3</e:mn></e:msub></e:math>; the ratio of the ground states of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mn>2</g:mn><g:mrow><g:mo>+</g:mo><g:mo>+</g:mo></g:mrow></g:msup></g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mn>0</i:mn><i:mrow><i:mo>+</i:mo><i:mo>+</i:mo></i:mrow></i:msup></i:math> channels are in full agreement with the lattice prediction. When considering <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>AdS</k:mi><k:mn>7</k:mn></k:msub></k:math> and the four-dimensional pure glue theory, a remarkably general picture emerges, where we can write formulas for the fluctuations that are in agreement with ones from holographic high-energy scattering and from <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi>AdS</m:mi><m:mo>/</m:mo><m:mi>CFT</m:mi></m:mrow></m:math> with IR and UV cutoff. We point out that this log branch in the IR in <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>D</o:mi></o:math> dimensions can be seen as the usual logarithmic branch of scalar fields saturating the Breitenlohner-Freedman bound in a conformally rescaled metric, with <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>AdS</q:mi><q:mrow><q:mi>D</q:mi><q:mo>−</q:mo><q:mn>1</q:mn></q:mrow></q:msub><q:mo>×</q:mo><q:msup><q:mi>S</q:mi><q:mn>1</q:mn></q:msup></q:math> asymptotics.