From $\mathrm{AdS}_5$ to $\mathrm{AdS}_3$: TsT deformations, Magnetic fields and Holographic RG Flows
It was previously shown that a D7 brane probe in a D3 brane background with a pure gauge constant magnetic field $\mathrm{B} = \mathrm{H}$ exhibits chiral symmetry breaking and a discrete meson spectrum with Zeeman splitting. In this work, we investigate how these features are modified by a TsT deformation of the background, which renders the Kalb Ramond field physical and radially dependent, thereby obscuring its interpretation as a constant magnetic field. We show that chiral symmetry breaking persists in the deformed model. The meson spectrum, however, depends on the fluctuation sector. Fluctuations perpendicular to the magnetic field are sensitive to the deformation and, for generic values of the TsT parameter $\mathrm{k}$, do not admit a consistent spectrum due to divergent behavior near the horizon, whereas fluctuations parallel to the magnetic field remain unaffected. Remarkably, the combined effect of the magnetic field and the TsT deformation singles out the special value $\mathrm{k} = -\frac{1}{\mathrm{H}}$. At this point, the perpendicular modes are restored. Moreover, the Kalb Ramond field becomes constant again, recovering its interpretation as a magnetic field. The resulting effects on the spectrum appear only at order $O(H^2)$, and therefore the Zeeman splitting, if present at all, is shifted to this higher order. Furthermore, the resulting background with $\mathrm{k} = - \frac{1}{\mathrm{H}}$ is interesting in its own right, even without embedding any brane. The spacetime admits an interpretation in terms of D1 branes and exhibits a degenerate boundary geometry, asymptotically $\mathrm{AdS}_3 \times S^5$, with a degenerate horizon. We present a first discussion of the dual field theory interpretation, making connections to D1 and D5 systems, renormalization group flow, defect field theories, and domain wall holography.