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We consider supersymmetric configurations in Type IIB supergravity obtained by the beackreaction of fundamental strings ending on a stack of D3-branes and smeared uniformly in the three spatial directions along the D3-branes. These automatically include a distribution of D5-brane baryon vertices necessary to soak up string charge. The backgrounds are static, preserving eight supersymmetries, an SO(5) global symmetry and symmetry under spatial translations and rotations. We obtain the most general BPS configurations consistent with the symmetries. We show that the solutions to the Type IIB field equations are completely specified by a single function (the dilaton) satisfying a Poisson-like equation in two dimensions. We further find that the equation admits a class of solutions displaying Lifshitz-like scaling with dynamical critical exponent z = 7. The equations also admit an asymptotically AdS5 × S5 solution deformed by the presence of backreacted string sources that yield a uniform density of heavy quarks in \( \mathcal{N}=4 \) SYM.

Emergent Lifshitz scaling from N = 4 $$ \mathcal{N}=4 $$ SYM with supersymmetric heavy-quark density