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Gauge theories from D7-branes over vanishing 4-cycles

Sebastian Franco, Gonzalo Torroba

TL;DR

This work analyzes gauge theories on D7-branes wrapped over vanishing 4-cycles in toric CY cones over del Pezzo surfaces, focusing on anomaly cancellation via O7-planes or flavor D7-branes and the resulting chiral, four-supercharged dynamics. It develops a comprehensive framework using brane tilings/dimer models to classify orientifolds (fixed points and lines) on $dP_0$ and extends to $dP_1$–$dP_3$, exploring geometric transitions, Seiberg duality, and nonperturbative effects in the presence of seven-branes. A central result is the identification of the Higgs/baryonic branch with fuzzy internal geometry arising from noncommutative instantons on the wrapped four-cycle, connecting to the F(uzz) theory limit of F-theory. The paper thus provides explicit anomaly-free quivers, orientifold classifications, and nonperturbative mechanisms that illuminate how seven-brane dynamics at CY singularities can realize fuzzy geometries and potential dualities in string compactifications.

Abstract

We study quiver gauge theories on D7-branes wrapped over vanishing holomorphic 4-cycles. We investigate how to incorporate O7-planes and/or flavor D7-branes, which are necessary to cancel anomalies. These theories are chiral, preserve four supercharges and exhibit very rich infrared dynamics. Geometric transitions and duality in the presence of O-planes are analyzed. We study the Higgs branch of these quiver theories, showing the emergence of fuzzy internal dimensions. This branch is related to noncommutative instantons on the divisor wrapped by the seven-branes. Our results have a natural application to the recently introduced F(uzz) limit of F-theory.

Gauge theories from D7-branes over vanishing 4-cycles

TL;DR

This work analyzes gauge theories on D7-branes wrapped over vanishing 4-cycles in toric CY cones over del Pezzo surfaces, focusing on anomaly cancellation via O7-planes or flavor D7-branes and the resulting chiral, four-supercharged dynamics. It develops a comprehensive framework using brane tilings/dimer models to classify orientifolds (fixed points and lines) on and extends to –, exploring geometric transitions, Seiberg duality, and nonperturbative effects in the presence of seven-branes. A central result is the identification of the Higgs/baryonic branch with fuzzy internal geometry arising from noncommutative instantons on the wrapped four-cycle, connecting to the F(uzz) theory limit of F-theory. The paper thus provides explicit anomaly-free quivers, orientifold classifications, and nonperturbative mechanisms that illuminate how seven-brane dynamics at CY singularities can realize fuzzy geometries and potential dualities in string compactifications.

Abstract

We study quiver gauge theories on D7-branes wrapped over vanishing holomorphic 4-cycles. We investigate how to incorporate O7-planes and/or flavor D7-branes, which are necessary to cancel anomalies. These theories are chiral, preserve four supercharges and exhibit very rich infrared dynamics. Geometric transitions and duality in the presence of O-planes are analyzed. We study the Higgs branch of these quiver theories, showing the emergence of fuzzy internal dimensions. This branch is related to noncommutative instantons on the divisor wrapped by the seven-branes. Our results have a natural application to the recently introduced F(uzz) limit of F-theory.

Paper Structure

This paper contains 21 sections, 78 equations, 12 figures.

Table of Contents

  1. Introduction and summary
  2. Quivers from wrapped D7-branes
  3. Anomaly cancellation: flavoring and orientifolding
  4. Review of the quiver for $dP_0$
  5. Gauge theory from seven-branes on $dP_0$
  6. Fixed point orientifolds
  7. Fixed line orientifolds
  8. Identifying and characterizing O7-planes
  9. Orientifolds of del Pezzo theories
  10. Orientifolds of $dP_1$
  11. Orientifolds of $dP_2$
  12. Orientifolds of $dP_3$
  13. Nonperturbative dynamics
  14. Geometric transitions with noncompact orientifolds
  15. Dual orientifold theories
  16. ...and 6 more sections

Figures (12)

  • Figure 1: Quiver diagram for $dP_0$.
  • Figure 2: One possible anomaly-free quiver diagram for $dP_0$ with $N_{D3}$ D3-branes, $N_{D7}$ D7-branes over the vanishing 4-cycle and $3N_{D7}$ non-compact flavor D7-branes.
  • Figure 3: Fixed point orientifold for $dP_0$.
  • Figure 4: Fixed line orientifold for $dP_0$.
  • Figure 5: Brane tiling for $dP_1$ with the orientifold fixed line.
  • ...and 7 more figures