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Surface defects in the D4 $-$ D8 brane system

Giuseppe Dibitetto, Nicolò Petri

TL;DR

The work constructs a new class of BPS flows in minimal $d=6$ $F(4)$ gauged supergravity with a running $2$-form, producing $AdS_3$-foliated geometries that asymptote to $AdS_6$ and uplift to warped $AdS_3\times S^2\times S^3$ solutions in massive IIA. Interpreted holographically, these flows describe surface defects (a $\mathcal{N}=(0,4)$ SCFT$_2$) within the $\mathcal{N}=2$ SCFT$_5$ dual to the $AdS_6\times S^4$ vacuum, arising from a D4-D8 brane system with a bound state of D2–NS5–D6 ending on it. The paper provides explicit analytic BPS solutions across four 6d backgrounds (with $M_3=\mathbb{R}^{1,2}$ or $AdS_3$ and $\Sigma_2=\mathbb{R}^2$ or $S^2$), their massive IIA uplifts, and a concrete holographic test via defect-induced one-point functions that match perturbative expectations. Overall, the results illuminate how AdS$_3$ slicing captures low-energy defect physics in higher-dimensional SCFTs and suggest links to lower-dimensional gauged supergravities describing similar defects. The constructions advance defect holography by connecting brane intersections to precise AdS$_3$-foliated loci within AdS$_6$ backgrounds and their IIA uplifts.

Abstract

A new class of exact supersymmetric solutions is derived within minimal $d = 6$ $F(4)$ gauged supergravity. These flows are all characterized by a non-trivial radial profile for the 2-form gauge potential included into the supergravity multiplet. In particular three solutions within this class are featured by an $\mathrm{AdS}_3$ foliation of the 6d background and by an $\mathrm{AdS}_6$ asymptotic geometry. Secondly, considering the simplest example of these, we give its massive IIA uplift describing a warped solution of the type $\mathrm{AdS}_3\times S^2\times S^3$ fibered over two intervals $I_r \times I_ξ$ . We interpret this background as the near-horizon of a D4 $-$ D8 system on which a bound state D2 $-$ NS5 $-$ D6 ends producing a surface defect. Finally we discuss its holographic dual interpretation in terms of a $\mathcal{N} = (0, 4)$ SCFT$_2$ defect theory within the $\mathcal{N} = 2$ SCFT$_5$ dual to the $\mathrm{AdS}_6\times S^4$ massive IIA warped vacuum.

Surface defects in the D4 $-$ D8 brane system

TL;DR

The work constructs a new class of BPS flows in minimal gauged supergravity with a running -form, producing -foliated geometries that asymptote to and uplift to warped solutions in massive IIA. Interpreted holographically, these flows describe surface defects (a SCFT) within the SCFT dual to the vacuum, arising from a D4-D8 brane system with a bound state of D2–NS5–D6 ending on it. The paper provides explicit analytic BPS solutions across four 6d backgrounds (with or and or ), their massive IIA uplifts, and a concrete holographic test via defect-induced one-point functions that match perturbative expectations. Overall, the results illuminate how AdS slicing captures low-energy defect physics in higher-dimensional SCFTs and suggest links to lower-dimensional gauged supergravities describing similar defects. The constructions advance defect holography by connecting brane intersections to precise AdS-foliated loci within AdS backgrounds and their IIA uplifts.

Abstract

A new class of exact supersymmetric solutions is derived within minimal gauged supergravity. These flows are all characterized by a non-trivial radial profile for the 2-form gauge potential included into the supergravity multiplet. In particular three solutions within this class are featured by an foliation of the 6d background and by an asymptotic geometry. Secondly, considering the simplest example of these, we give its massive IIA uplift describing a warped solution of the type fibered over two intervals . We interpret this background as the near-horizon of a D4 D8 system on which a bound state D2 NS5 D6 ends producing a surface defect. Finally we discuss its holographic dual interpretation in terms of a SCFT defect theory within the SCFT dual to the massive IIA warped vacuum.

Paper Structure

This paper contains 20 sections, 125 equations, 6 tables.

Table of Contents

  1. Introduction
  2. The D4-D8 System and $\hbox{$\mathrm{AdS}$}_6/\hbox{$\mathrm{CFT}$}_5$
  3. Including a NUT Charge
  4. The Supergravity Setup
  5. Minimal $\hbox{$\mathcal{N}$}=(1,1)$ Gauged Supergravity in $d=6$
  6. $\hbox{$\mathrm{AdS}$}_6$ Vacuum and Domain Walls
  7. The Massive IIA Origin of $F(4)$ Supergravity
  8. BPS Flows with the 2-form Gauge Potential
  9. The General Ansatz
  10. Background with $M_3=\mathbb{R}^{1,2}$ and $\Sigma_2=\mathbb{R}^{2}$
  11. Background with $M_3=\mathrm{AdS}_3$ and $\Sigma_2=\mathbb{R}^{2}$
  12. Background with $M_3=\mathbb{R}^{1,2}$ and $\Sigma_2=S^{2}$
  13. Background with $M_3=\hbox{$\mathrm{AdS}$}_3$ and $\Sigma_2=S^{2}$
  14. Surface Defects within the $\hbox{$\mathcal{N}$}=2$ $\hbox{$\mathrm{SCFT}$}_5$
  15. Charged Domain Wall and Massive IIA Uplift
  16. ...and 5 more sections