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Conifold Transitions and Five-Brane Condensation in M-Theory on Spin(7) Manifolds

Sergei Gukov, James Sparks, David Tong

TL;DR

This work identifies and analyzes a nontrivial topology-changing transition in M-theory on Spin(7) manifolds, centered on a conifold-like singularity at the cone over $SU(3)/U(1)$. It develops a unified picture in which the transition is realized by condensation of wrapped brane states (M5 in M-theory, D6 in IIA) and is mirrored by brane/flux dualities, parity flips, and three-branch moduli tied to half-integer $G$-flux. The authors connect geometric transitions to low-energy Chern–Simons–Higgs dynamics in three dimensions, show how two distinct Type IIA dual pictures (B-picture and L-picture) encode the same physics, and provide explicit constructions of the relevant quotients and coassociative loci. The results illuminate how topology, flux quantization, and brane dynamics intertwine in reduced-supersymmetry settings, offering a first explicit example of a Spin(7) conifold transition with only 1/16 supersymmetry and broad implications for brane/flux dualities and holographic flows.

Abstract

We conjecture a topology changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a CP(2) bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping the 5-sphere. Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G_2 holonomy manifold with either wrapped D6-branes, or background Ramond-Ramond flux. This is the first non-trivial example of a topology changing transition with only 1/16 supersymmetry.

Conifold Transitions and Five-Brane Condensation in M-Theory on Spin(7) Manifolds

TL;DR

This work identifies and analyzes a nontrivial topology-changing transition in M-theory on Spin(7) manifolds, centered on a conifold-like singularity at the cone over . It develops a unified picture in which the transition is realized by condensation of wrapped brane states (M5 in M-theory, D6 in IIA) and is mirrored by brane/flux dualities, parity flips, and three-branch moduli tied to half-integer -flux. The authors connect geometric transitions to low-energy Chern–Simons–Higgs dynamics in three dimensions, show how two distinct Type IIA dual pictures (B-picture and L-picture) encode the same physics, and provide explicit constructions of the relevant quotients and coassociative loci. The results illuminate how topology, flux quantization, and brane dynamics intertwine in reduced-supersymmetry settings, offering a first explicit example of a Spin(7) conifold transition with only 1/16 supersymmetry and broad implications for brane/flux dualities and holographic flows.

Abstract

We conjecture a topology changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a CP(2) bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping the 5-sphere. Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G_2 holonomy manifold with either wrapped D6-branes, or background Ramond-Ramond flux. This is the first non-trivial example of a topology changing transition with only 1/16 supersymmetry.

Paper Structure

This paper contains 18 sections, 154 equations, 13 figures, 1 table.

Table of Contents

  1. Introduction
  2. D6-Branes, M-Theory and $Spin(7)$ Conifolds
  3. D6-Branes and the Cone over $SO(5)/SO(3)$
  4. D6-Branes and the Cone over $SU(3)/U(1)$
  5. Deformations of Coassociative Cones
  6. Anomalies and Supersymmetry
  7. Flux at Infinity
  8. Parity Transformations
  9. Low-Energy Dynamics and Condensation of Five-Branes
  10. Type II Strings on Manifolds of $G_2$ Holonomy
  11. The Cone over $\bf \mathbb{C}P^3$
  12. The Cone over $SU(3)/U(1)^2$
  13. M-theory on the $Spin(7)$ Cone over $SU(3)/U(1)$
  14. Geometric Quotients
  15. Brane/Flux Transitions
  16. ...and 3 more sections

Figures (13)

  • Figure 1: Conifold transition in type IIB string theory.
  • Figure 2: Conifold transition in M-theory on a manifold with $Spin(7)$ holonomy.
  • Figure 3: Geometric transition as a conifold transition in M-theory on $Spin(7)$ manifold.
  • Figure 4: A curve in the $r-s$ plane, whose $Sp(1)$ orbits sweep out coassociative submanifolds: A) the singular cone over a squashed three-sphere, and B) $L=H^1$.
  • Figure 5: A curve in the $r-s$ plane whose $Sp(1)$ orbits sweep out coassociative submanifolds: A) $L = {\bf S}^3 \times \mathbb{R}$, B) the singular cone, and C) $L=H^1\cup \mathbb{R}^4$
  • ...and 8 more figures