Mesons in Gauge/Gravity Duals - A Review

TL;DR

The review surveys how mesons emerge in gauge/gravity duality by embedding flavour through D7 branes and other brane configurations, enabling a holographic description of quark bound states in strongly coupled gauge theories. It presents both top-down constructions (D3/D7 and related systems) and bottom-up AdS/QCD approaches, highlighting dynamical chiral symmetry breaking, Goldstone modes, and meson spectra, including heavy-light states and high-spin Regge trajectories. Finite-temperature holography and meson melting are examined via AdS black-hole backgrounds, while backreaction and non-supersymmetric settings are explored to approach QCD-like physics. Overall, the work demonstrates that holographic methods capture a broad range of QCD-like phenomena with quantitative connections to lattice and experimental data, while also clarifying the limitations and regime of validity of the duality in real-world QCD.

Abstract

We review recent progress in studying mesons within gauge/gravity duality, in the context of adding flavour degrees of freedom to generalizations of the AdS/CFT correspondence. Our main focus is on the `top-down approach' of considering models constructed within string theory. We explain the string-theoretical constructions in detail, aiming at non-specialists. These give rise to a new way of describing strongly coupled confining large N gauge gauge theories similar to large N QCD. In particular, we consider gravity dual descriptions of spontaneous chiral symmetry breaking, and compare with lattice results. A further topic covered is the behaviour of flavour bound states in finite temperature field theories dual to a gravity background involving a black hole. We also describe the `bottom up' phenomenological approach to mesons within AdS/QCD. -- Some previously unpublished results are also included.

Figures (31)

• Figure 2.1: Schematic representation of the AdS/CFT duality. The D3 branes warp the space into a throat whose near-horizon geometry is $AdS_5 \times S^5$. Asymptotically, far away from the branes the geometry returns to flat ten-dimensional space. Open string degrees of freedom on the D3 branes, which give rise to ${\cal N}=4$$SU(N)$ Super Yang-Mills theory, are mapped to closed string excitations in the $AdS_5 \times S^5$ near-horizon geometry.
• Figure 2.2: Three important configurations of strings connecting sources on a probe brane. In AdS the strings from two sources prefer to join than fall independently to $r=0$. They dip further into the space the more the quarks are separated. In a confining geometry a blockage forces the string to lie along the blockage and the energy scales with the separation. Finite temperature is reproduced by a black hole horizon - once the strings fall in, the quarks are screened from each other.
• Figure 3.1: Schematic representation of the AdS/CFT duality with added flavour. In addition to the original AdS/CFT duality, open string degrees of freedom representing quarks are mapped to open strings beginning and ending on the D7 probe, which asymptotically near the boundary wrap $AdS_5\times S^3$ inside $AdS_5\times S^5$. For simplicity, the five-sphere is not drawn in this picture.
• Figure 3.2: Gravity dual in presence of a fundamental hypermultiplet with finite mass $m$. The D7 brane probe is shown in blue. In this case, the radius of the $S^3$ wrapped by the D7 brane probe becomes a function of the AdS radial direction $r$. At $r=L$, the radius of the $S^3$ shrinks to zero, and the D7 probe does not extend any further into the interior of AdS space. (Figure by Zachary Guralnik, from Babington:2003vm.)
• Figure 3.3: Fluctuations of the $S^3$ wrapped by the D7 probe inside $S^5$. These modes give rise to the meson masses.