Holographic interpolations of defect CFTs

TL;DR

The paper introduces a holographic duality for a class of non-supersymmetric defect CFTs realized by a D5-brane probe in $AdS_5\times S^5$, wrapping an $S^2$ and extending to $AdS_3\times S^1$, and it is terminated by two D7-branes to cancel gauge anomalies. The solution is controlled by two continuous parameters, $\sigma$ and $\rho$, and interpolates between the 1/2-BPS D3-D3 defect and a non-supersymmetric D3-D5-like phase, with stability established via a BF bound analysis in a defined region of parameter space. The authors compute the holographic one-point functions of chiral primary operators and elucidate the dual field theory picture, proposing non-supersymmetric co-dimension-2 defect operators in ${\cal N}=4$ SYM that couple to bulk fields through a defect gauge field, Wilson-line structures, and defect hypermultiplet vevs. The work thus extends holographic dCFT constructions beyond SUSY, connecting known SUSY defects to new non-SUSY configurations and outlining clear directions for cross-checks and extensions, including anomaly coefficients, higher-point correlators, and duality properties. Overall, the paper provides a concrete gravity-side construction, a careful stability/anomaly analysis, and a detailed field-theory interpretation of a novel class of defect holographies with potential broad impact in AdS/dCFT studies.

Abstract

We propose a new class of holographic dualities between certain, generically non supersymmetric, defect conformal field theories (dCFTs) and their gravity duals. Our construction interpolates between the 1/2-BPS D3-D3 system and its field theory dual at one end, and the holographic duality presented in arXiv: 2506.14505 at the other. On the gravity side, the defect is realised by a novel D5 probe brane embedded in the $AdS_5\times S^5$ geometry. The symmetry of the induced on the D5 brane metric is $AdS_3\times S^1\times S^2$. At a certain limit the D5 brane becomes singular and resembles the D3-D3 system. Consistency requires the presence of two D7 branes on which the D5 brane terminates. The existence of boundaries induces a gauge anomaly for the D5 brane which is cancelled through anomaly inflow from the D7 branes. The full system of the D5 and D7 branes is, thus, anomaly free. Also it does not have any tachyonic instabilities for a certain range of its parameters. On the field theory side, we determined the classical solution of the ${\cal N}=4$ SYM equations of motion which we conjecture to describe the defect dual to the D5-D7 system and comment on the identification of the parameters appearing at the two sides of the duality.

Figures (7)

• Figure 1: A graph depicting the portion of the parametric space $(\sigma,\rho)$ for which our solution is valid. The two red lines correspond to the limiting curves that are presented in equation \ref{['boundss']} and the dotted magenta line is for the value $\sigma = 2\sqrt{2}$.
• Figure 2: A picture depicting the D5 brane. The yellow cone is the D5 brane. The point at which the cone touches the boundary $z=0$ is really a two dimensional surface since the coordinates $x_0$ and $x_1$, along which the brane extends, have been suppressed. The blue horizontal plane is parametrised by the coordinates $(x_2,x_3)=(r \cos{\psi},r \sin{\psi})$ and represents the boundary of the $AdS_5$ space with the vertical axis being the holographic coordinate $z$. The green and red vertical planes represent the two D7 branes. The D5 brane has one of its boundaries on the green D7 brane and the other on the red one. The D5 starts from the red D7, winds anticlockwise once or more times around the $\psi$ angle and ends on the green D7 brane. The necessity of the D7 branes is discussed in section \ref{['D5-D7']}.
• Figure 3: On the left graph we have drawn the function $m^2_1(\rho,\sigma)+1$ for the range of $\sigma \in [0,2 \sqrt{2}]$ subject to the condition \ref{['boundss']}. We have allowed $\rho$ to be between $1$ and $3.5$. The blue plane is the zero of the vertical axis $z=0$. On the right graph we have drawn the function $m^2_2(\rho,\sigma)+1$ for the same values of $\rho$ and $\sigma$.
• Figure 4: On the left graph we have drawn the portion of the $(\rho,\sigma)$ plane for which the masses of the coupled fluctuations $\delta z$ and $\delta \tilde{\psi}$ are above the B-F bound, always subject to the condition \ref{['boundss']}. As in figure \ref{['figg-2']}, $\sigma \in [0,2 \sqrt{2}]$ while $1< \rho \le 3$. On the right graph we have further imposed the constraint \ref{['co-2']}. This is the final area in which $\rho$ and $\sigma$ can take values so that all masses are above the B-F bound.
• Figure 5: On the left graph we have drawn the function $m^2_1(\rho,\sigma)+1$ for the range of $\sigma\geq 2 \sqrt{2}$ subject to the condition \ref{['boundss']}. We have allowed $\rho$ to be between $1$ and $3.5$. The blue plane is the zero of the vertical axis $z=0$. On the right graph we have drawn the function $m^2_2(\rho,\sigma)+1$ for the same values of $\rho$ and $\sigma$.