From $\mathrm{AdS}_5$ to $\mathrm{AdS}_3$: TsT deformations, Magnetic fields and Holographic RG Flows

TL;DR

The work investigates TsT deformations of a D3–D7 holographic setup with a constant magnetic field to assess changes in chiral symmetry breaking and meson spectra. It finds that chiral symmetry breaking persists under deformation, but the meson spectrum splits into a deformation-sensitive perpendicular sector (ill-defined for generic $k$) and an undeformed-parallel sector (invariant under TsT), with a special case $k=-1/H$ restoring the perpendicular modes and yielding a magnetic interpretation again. A remarkable emergent background at this special value reduces to a D1-brane system with an asymptotically AdS$_3 imes S^5$ boundary, suggesting an anisotropic RG flow from a UV $d=2$ theory to a strongly coupled IR regime and tying the setup to defect/domain-wall holography. The dual field theory interpretation points to nonlocal interactions and possible non-commutative features, captured by degenerate boundary geometry and anisotropic scaling. Overall, the paper extends AdS/CFT phenomenology by revealing how TsT-induced non-constancy in the Kalb–Ramond field shapes IR physics while preserving key IR phenomena like chiral symmetry breaking, and it opens avenues to study 2D holography within D1/D5–type sectors and defect theories.

Abstract

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.

Figures (4)

• Figure 1: Sequence of deformations of the original model and the corresponding loss of symmetries.
• Figure 2: The TsT deforming of the D3-D7 + $\mathrm{H}$ constant Filev_2007 model in different regime of energies.
• Figure 3: The background as the radius coordinates increases, the planes representing the spacelike domain-walls.
• Figure 4: The dual field theory can be interpreted as an energy flow, where the intermediate regime is effectively four dimensional, while the asymptotic behavior is properly described by a two dimensional theory. One should not take the image literally, as the asymptotic models are not RG fixed point.