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Dynamic SU(2) Structure from Seven-branes

Ben Heidenreich, Liam McAllister, Gonzalo Torroba

TL;DR

The work derives explicit local type IIB supergravity solutions with dynamic SU(2) structure near a stack of four D7-branes and an O7-plane on a rigid four-cycle, interpreting deformations toward generalized complex geometry as arising from nonperturbative seven-brane dynamics. By focusing on a near-stack region and a Calabi-Yau cone over P^2, the authors obtain a closed-form AdS-like solution in a framework that is SL(2,R) covariant, and they analyze the SUSY conditions, fluxes, and the D3-brane charge both near the stack and in the full cone. The results illuminate how gaugino condensation on seven-branes can backreact via IASD flux in ten dimensions, link to R-symmetry breaking and domain walls, and offer potential applications to KKLT consistency and del Pezzo transitions in flux compactifications. The work provides a concrete, controllable setting to study the ten-dimensional imprint of nonperturbative seven-brane physics and its role in moduli stabilization.

Abstract

We obtain a family of supersymmetric solutions of type IIB supergravity with dynamic SU(2) structure, which describe the local geometry near a stack of four D7-branes and one O7-plane wrapping a rigid four-cycle. The deformation to a generalized complex geometry is interpreted as a consequence of nonperturbative effects in the seven-brane gauge theory. We formulate the problem for seven-branes wrapping the base of an appropriate del Pezzo cone, and in the near-stack limit in which the four-cycle is flat, we obtain an exact solution in closed form. Our solutions serve to characterize the local geometry of nonperturbatively-stabilized flux compactifications.

Dynamic SU(2) Structure from Seven-branes

TL;DR

The work derives explicit local type IIB supergravity solutions with dynamic SU(2) structure near a stack of four D7-branes and an O7-plane on a rigid four-cycle, interpreting deformations toward generalized complex geometry as arising from nonperturbative seven-brane dynamics. By focusing on a near-stack region and a Calabi-Yau cone over P^2, the authors obtain a closed-form AdS-like solution in a framework that is SL(2,R) covariant, and they analyze the SUSY conditions, fluxes, and the D3-brane charge both near the stack and in the full cone. The results illuminate how gaugino condensation on seven-branes can backreact via IASD flux in ten dimensions, link to R-symmetry breaking and domain walls, and offer potential applications to KKLT consistency and del Pezzo transitions in flux compactifications. The work provides a concrete, controllable setting to study the ten-dimensional imprint of nonperturbative seven-brane physics and its role in moduli stabilization.

Abstract

We obtain a family of supersymmetric solutions of type IIB supergravity with dynamic SU(2) structure, which describe the local geometry near a stack of four D7-branes and one O7-plane wrapping a rigid four-cycle. The deformation to a generalized complex geometry is interpreted as a consequence of nonperturbative effects in the seven-brane gauge theory. We formulate the problem for seven-branes wrapping the base of an appropriate del Pezzo cone, and in the near-stack limit in which the four-cycle is flat, we obtain an exact solution in closed form. Our solutions serve to characterize the local geometry of nonperturbatively-stabilized flux compactifications.

Paper Structure

This paper contains 39 sections, 192 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Gaugino condensation in string compactifications
  3. Nonperturbative effects from seven-branes and generalized complex geometry
  4. Overview
  5. Seven-branes and Orientifolds
  6. Orientifolds of resolved del Pezzo cones
  7. The Calabi-Yau geometry of the $\mathbb{P}^2$ cone
  8. Ansatz for the Supergravity Solution
  9. The near-stack region
  10. Seven-branes in the $\mathbb{P}^2$ cone
  11. Metric ansatz for the $\mathbb{P}^2$ cone
  12. Kählerity and the Calabi-Yau metric
  13. $G_3$ ansatz for the $\mathbb{P}^2$ cone
  14. D3-brane charge
  15. The near-stack limit of the $\mathbb{P}^2$ cone
  16. ...and 24 more sections

Figures (2)

  • Figure 1: $(c_3,c_4,c_5)$ parameter space. The region inside the cones is excluded. The surface of the negative cone is also excluded, whereas the surface of the positive cone consists of constant dilaton solutions. Hyperbolae of constant $c_3\,c_4$ are related by radial rescaling.
  • Figure 2: The singularity structure of the constant dilaton solutions. The horizontal axis is $r/r_{\star}$ and the vertical axis is $\delta$. The nonsingular region is unshaded and $\Xi_+$ ($\Xi_-$) is negative in the blue (red) region. The first (second) plot corresponds to positive (negative) $Q$.