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6d surface defects from massive type IIA

Giuseppe Dibitetto, Nicolò Petri

TL;DR

The authors construct a novel BPS flow in seven-dimensional minimal N=1 supergravity with SU(2) gauging and a dyonic 3-form profile, producing an AdS$_3$-sliced background that uplifts to a warped AdS$_3$ geometry in massive type IIA. They interpret this gravity solution as holographically describing a conformal surface defect (SCFT$_2$) within the six-dimensional $ ext{N}=(1,0)$ theory dual to AdS$_7$. The defect is realized in string theory by D2- and wrapped D4-branes ending on the NS5–D6–D8 funnel, and the paper provides the detailed 10d uplift and brane picture, including an analysis of nonzero one-point functions for a dimension-4 operator on the defect. The work opens avenues to compute the displacement operator and to realize smooth interpolations between AdS$_3$ in the IR and AdS$_7$ in the UV, deepening the holographic understanding of lower-dimensional defects in higher-dimensional SCFTs.

Abstract

We present a new BPS flow within minimal $\mathcal{N}=1$ supergravity in seven dimensions describing a warped $\textrm{AdS}_{3}$ background supported by a "dyonic" profile of the three-form. Furthermore, we discuss the holographic interpretation of the above solution in terms of a defect $\textrm{SCFT}_{2}$ inside the 6d $(1,0)$ theory dual to the AdS in the asymptotic region. Finally we provide the brane picture of the aforementioned defect CFT as D2- and wrapped D4-branes ending on a D6 - NS5 - D8 funnel in massive type IIA string theory.

6d surface defects from massive type IIA

TL;DR

The authors construct a novel BPS flow in seven-dimensional minimal N=1 supergravity with SU(2) gauging and a dyonic 3-form profile, producing an AdS-sliced background that uplifts to a warped AdS geometry in massive type IIA. They interpret this gravity solution as holographically describing a conformal surface defect (SCFT) within the six-dimensional theory dual to AdS. The defect is realized in string theory by D2- and wrapped D4-branes ending on the NS5–D6–D8 funnel, and the paper provides the detailed 10d uplift and brane picture, including an analysis of nonzero one-point functions for a dimension-4 operator on the defect. The work opens avenues to compute the displacement operator and to realize smooth interpolations between AdS in the IR and AdS in the UV, deepening the holographic understanding of lower-dimensional defects in higher-dimensional SCFTs.

Abstract

We present a new BPS flow within minimal supergravity in seven dimensions describing a warped background supported by a "dyonic" profile of the three-form. Furthermore, we discuss the holographic interpretation of the above solution in terms of a defect inside the 6d theory dual to the AdS in the asymptotic region. Finally we provide the brane picture of the aforementioned defect CFT as D2- and wrapped D4-branes ending on a D6 - NS5 - D8 funnel in massive type IIA string theory.

Paper Structure

This paper contains 6 sections, 25 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. 6d $(1,0)$ SCFT's from massive type IIA
  3. A new BPS flow in minimal $\mathcal{N}=1$ 7d supergravity
  4. Massive type IIA brane picture
  5. One-point correlation functions
  6. Conclusions

Figures (2)

  • Figure 1: The brane picture of the linear quiver realizing the above $(1,0)$ SCFT's. In this diagram the $x^{6}$ coordinate represents $z$, while the directions $x^{7,8,9}$ are to be identified with $(r,\theta^{1},\theta^{2})$. D8-branes are vertical lines, D6-branes are horizontal lines, and finally the "fat" bubbles represent point-like NS5-branes which collide at the fixed point.
  • Figure 2: The three different limits of the brane system represented in \ref{['brane_sol']} depending on the three coordinates $(\rho,z,r)$, respectively yielding $\textrm{AdS}_{7}$, the asymptotic domain-wall behavior typical of massive type IIA solutions, and $\textrm{AdS}_{3}$. Each limit is controlled by a different combination of the above cooridnates.