This set-up occurs when the brane degrees of freedom are responsible for either breaking the symmetries of the larger system or describing an interesting isolated set of massless degrees of freedom whose interactions among themselves and with the background one is interested in studying. In the following, I very briefly describe how the first approach was used to introduce flavour in the AdS/CFT correspondence, and how the second one can be used to study physics reminiscent of certain phenomena in condensed-matter systems.
As an example, consider the addition of flavour in the standard AdS/CFT. It was argued in  that this could be achieved by adding D7-branes to a background of D3-branes. The D7-branes give rise to fundamental hypermultiplets arising from the lightest modes of the 3-7 and 7-3 strings, in the brane arraydynamical quarks is given by , where is the distance between the D3- and the D7-branes in the 89-plane. If the D3-branes may be replaced (in the appropriate decoupling limit) by an AdS5 × S5 geometry, as in the standard AdS/CFT argument, whereas if, in addition, then the back-reaction of the D7-branes on this geometry may be neglected. Thus, one is left, in the gravity description, with D7-brane probes in AdS5 × S5. In the particular case of , one can use the effective action described before. This specific set-up was used in  to study the linearised fluctuation equations for the different excitations on the D7-probe describing different scalar and vector excitations to get analytical expressions for the spectrum of mesons in SYM, at strong coupling.
This logic can be extended to non-supersymmetric scenarios44. For example, using the string theory realisation of four-dimensional QCD with colours and flavours discussed in . The latter involves D6-brane probes in the supergravity background dual to D4-branes compactified on a circle with supersymmetry-breaking boundary conditions and in the limit in which all the resulting Kaluza–Klein modes decouple. For and for massless quarks, spontaneous chiral symmetry breaking by a quark condensate was exhibited in  by working on the D6-brane effective action in the near horizon geometry of the D4-branes.
Similar considerations apply at finite temperature by using appropriate black-hole backgrounds  in the relevant probe action calculations. This allows one to study phase transitions associated with the thermodynamic properties of the probe degrees of freedom as a function of the probe location. This can be done in different theories, with flavour , and for different ensembles [343, 378].
The amount of literature in this topic is enormous. I refer the reader to the reviews on the use of gauge-gravity duality to understand hot QCD and heavy ion collisions  and meson spectroscopy , and references therein. These explain the tools developed to apply the AdS/CFT correspondence in these set-ups.
One interesting possibility involving this mechanism consists on the emergence of gauge fields (“photons”) at the onset of such critical phases. For example, 2 + 1 Maxwell theory in the presence of a Fermi surface (chemical potential )
The general set-up, based on the discussions appearing, among others, in [334, 398, 286], is as follows. One considers a small set of charged degrees of freedom, provided by the probe “flavour” brane, interacting among themselves and with a larger set of neutral quantum critical degrees of freedom having Lifshitz scale invariance with dynamical critical exponent . As in previous applications, the latter is replaced by a gravitational holographic dual with Lifshitz asymptotics [162, 370, 102, 34]
In practice, one embeds the probe “flavour” brane in the spacetime holographic dual, which may include some non-trivial cycle wrapping in internal dimensions when embedded in string theory, and turns on some non-trivial electric and magnetic fluxes on the branep-brane action. As in any thermodynamic system, observables such as specific heat or magnetic susceptibility can be computed from Eq. (469) by taking appropriate partial derivatives. Additionally, transport observables, such as DC, AC or DC Hall conductivities can also be computed and studied as a function of the background, probe embedding and the different constants controlling the world volume gauge field (468).
More than the specific physics, which is nicely described in [334, 398, 286], what is important to stress, once more, is that using the appropriate backgrounds, exciting the relevant degrees of freedom and considering the adequate boundary conditions make the methods described in this review an extremely powerful tool to learn about physics in regimes of parameters that would otherwise be very difficult to handle, both analytically and conceptually.
Living Rev. Relativity 15, (2012), 3
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