[Paper Review] Glueball Masses from Supergravity with Flavor

Kenji Suzuki|ArXiv.org|Nov 7, 2004

Black Holes and Theoretical Physics4 citations

TL;DR

This paper computes glueball masses in a four-dimensional ${\cal N}=2$ super Yang-Mills theory with fundamental matter using the supergravity dual of D3/D7 branes. It numerically solves wave equations for scalar and antisymmetric tensor fields in the background, finding that $0^{++}$ glueball masses agree with lattice QCD results and that the $M_{GB}/M_{\text{meson}}$ ratio is approximately 1.4, consistent with large-$N$ expectations.

ABSTRACT

We study the glueballs in a four-dimensional ${\cal N}=2$ super Yang-Mills theory with fundamental matters in terms of the supergravity dual. The supergravity background is constructed by $N$ D3 brane with a probe D7 brane. We numerically compute the glueball masses for $0^{++}$ and $1^{--}$ in the background. We find that the mass ratio of $0^{++}$ glueballs is mostly in agreement with the lattice calculations. We compare the glueball masses with the meson masses. The mass ratio $M_{GB}/M_{meson}$ is calculated with 1.4. If the mass $M_{GB}$ is set to $1.6 GeV$, the meson mass $M_{meson}$ is given with $1.1 GeV$.

Motivation & Objective

• To study glueball spectra in a four-dimensional ${\cal N}=2$ super Yang-Mills theory with fundamental hypermultiplets using the AdS/CFT correspondence.
• To compute glueball masses numerically in the supergravity background dual to $N$ D3-branes with a probe D7-brane.
• To compare the computed glueball masses with lattice QCD results and meson masses in the same background.
• To investigate the dependence of glueball masses on the quark mass and the mass ratio $M_{GB}/M_{\text{meson}}$.

Proposed method

• Construct the supergravity background from $N$ D3-branes and a probe D7-brane, with the D7-brane's position determining the quark mass.
• Solve the scalar wave equation for the dilaton in the background to obtain the $0^{++}$ glueball spectrum numerically.
• Use the RR 2-form field equation to compute the $1^{--}$ glueball spectrum via numerical shooting from large $\rho$ to $\rho=0$.
• Compare the resulting glueball masses with lattice QCD data and with results from the Klebanov-Strassler background.
• Evaluate the mass ratio $M_{GB}/M_{\text{meson}}$ and relate it to the tension ratio $T_{adj}/T_{QCD}$ in the large-$N$ limit.

Experimental results

Research questions

• RQ1 How do the $0^{++}$ glueball masses in the D3/D7 supergravity background compare with lattice QCD calculations?
• RQ2 What is the numerical value of the mass ratio $M_{GB}/M_{\text{meson}}$ in this ${\cal N}=2$ theory with fundamental matter?
• RQ3 How do the glueball masses depend on the quark mass parameter in the D7-brane setup?
• RQ4 How does the $1^{--}$ glueball spectrum in the D3/D7 background compare with that in the ${\cal N}=1$ Klebanov-Strassler background?

Key findings

• The $0^{++}$ glueball masses computed numerically are in good agreement with lattice QCD results, particularly for the lightest states.
• The mass ratio $M_{GB}/M_{\text{meson}}$ is found to be approximately 1.4, independent of the quark mass.
• This ratio is consistent with the large-$N$ expectation $\sqrt{2N^2/(N^2-1)} \approx 1.4$ from the ratio of adjoint and fundamental string tensions.
• The $1^{--}$ glueball spectrum is computed numerically, with the lightest state at $MR^2/m \approx 4.7$.
• The $M_{1^{--}}/M_{0^{++}}$ ratio is 1.15 in the D3/D7 background, close to the 1.20 value in the Klebanov-Strassler ${\cal N}=1$ background.
• Glueball masses are found to be proportional to the quark mass, as encoded in the D7-brane position.