Three-dimensional super Yang-Mills with compressible quark matter

Abstract

Abstract:We construct the gravity dual of three-dimensional, SU(N c ) super Yang-Mills theory with N f flavors of dynamical quarks in the presence of a non-zero quark density N q . The supergravity solutions include the backreaction of N c color D2-branes and N f flavor D6-branes with N q units of electric flux on their worldvolume. For massless quarks, the solutions depend non-trivially only on the dimensionless combination ρ = N 2 c N q /λ 2 N 4 f , with λ = g 2 YM N c the 't Hooft coupling, and describe renormalization group flows between the super Yang-Mills theory in the ultraviolet and a non-relativistic theory in the infrared. The latter is dual to a hyperscaling-violating, Lifshitz-like geometry with dynamical and hyperscaling-violating exponents z = 5 and θ = 1, respectively. If ρ 1 then at intermediate energies there is also an approximate AdS 4 region, dual to a conformal Chern-SimonsMatter theory, in which the flow exhibits quasi-conformal dynamics. At zero temperature we compute the chemical potential and the equation of state and extract the speed of sound. At low temperature we compute the entropy density and extract the number of low-energy degrees of freedom. For quarks of non-zero mass M q the physics depends non-trivially on ρ and M q N c /λN f .

Towards a holographic quark matter crystal

“…To see the relation between the first term in (2.18) and the string density we turn to the equation of motion for the B-field: 19) with S the total supergravity-plus-sources action. This may be written as 20) with…”

“…[18][19][20][21], we follow [12] and work with a RR charge quantized in units of N c instead of g s N c (for a comparison between both normalizations, see e.g. section 4.1 of [22]).…”

Breaking the sound barrier in holography

“…This might change upon considering the backreaction of the branes. Solutions with backreacted flavors at finite density have been recently constructed in [57][58][59][60]. Another possibility is to take an alternative large-N limit where …”

Flavours and infra-red instability in holography

“…Thus, there is reason to believe that, within a precise and complete D-brane picture, however rich the structure may be, the essential physics of instabilities that we have considered here, can be captured by rather simple reduced models that we have discussed here. We conclude this discussion by noting that, the models studied in [27][28][29][30][31] may present natural candidates for a stringy-embedding of the type we have alluded to. Perhaps more of the corresponding phase diagram and equations of state can also be explored within these models.…”