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Semi Localized Brane Intersections in SUGRA

A. Loewy

TL;DR

The paper tackles constructing semi-localized brane intersections in supergravity by allowing one harmonic function to depend on relative transverse coordinates, enabling a controlled interpolation between fully smeared and fully localized configurations. It derives explicit SUGRA solutions for NS–Dp and Dp–NS intersections, solving curved-space Laplace equations for the localized harmonic functions and analyzing their near-horizon geometries. The work connects these geometries to dual gauge theories across dimensions, including 4D $ ext{$ abla$-}$, 2+1D, and 1+1D theories with various hypermultiplet content, and explores duality webs via M-theory uplifts, S-duality, and T-duality, as well as orbifold constructions. It discusses Wilson-loop observables and the interpretation of these dualities, while noting that a full field-theory description for general Dp–Dp and certain configurations remains an open challenge.

Abstract

We construct SUGRA solutions of brane configurations of intersecting Dp and NS branes. These solutions are semi-localized in the sense that one of the intersecting branes is smeared along the world volume of the other, while the second is localized. We examine the gauge theory that lives on the localized brane, and the various descriptions possible via T and S dualities, and M-theory.

Semi Localized Brane Intersections in SUGRA

TL;DR

The paper tackles constructing semi-localized brane intersections in supergravity by allowing one harmonic function to depend on relative transverse coordinates, enabling a controlled interpolation between fully smeared and fully localized configurations. It derives explicit SUGRA solutions for NS–Dp and Dp–NS intersections, solving curved-space Laplace equations for the localized harmonic functions and analyzing their near-horizon geometries. The work connects these geometries to dual gauge theories across dimensions, including 4D abla, 2+1D, and 1+1D theories with various hypermultiplet content, and explores duality webs via M-theory uplifts, S-duality, and T-duality, as well as orbifold constructions. It discusses Wilson-loop observables and the interpretation of these dualities, while noting that a full field-theory description for general Dp–Dp and certain configurations remains an open challenge.

Abstract

We construct SUGRA solutions of brane configurations of intersecting Dp and NS branes. These solutions are semi-localized in the sense that one of the intersecting branes is smeared along the world volume of the other, while the second is localized. We examine the gauge theory that lives on the localized brane, and the various descriptions possible via T and S dualities, and M-theory.

Paper Structure

This paper contains 9 sections, 31 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Semi-localized NS branes
  3. NS $\bot$ D4
  4. NS $\bot$ D3
  5. NS $\bot$ D2
  6. NS $\bot$ D1
  7. Semi-localized Dp branes
  8. Summary and discussion
  9. Acknowledgments.

Figures (1)

  • Figure 1: A smeared NS-brane as the continuum limit of a periodic array of NS-branes. The D4-brane is stretched along the compact coordinate 6. Other Dp-brane configurations are similar.