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Supersymmetry Breaking from a Calabi-Yau Singularity

D. Berenstein, C. P. Herzog, P. Ouyang, S. Pinansky

TL;DR

The paper proposes a geometric criterion, SUSY-BOG, for spontaneous supersymmetry breaking in string backgrounds with Calabi-Yau singularities and wrapped branes, focusing on obstructions to complex structure deformations. It analyzes the cone over the first del Pezzo surface, dP1, via its dual gauge theory (Y^{2,1}) and shows that while gaugino condensation deforms the chiral ring, the deformation is obstructed, preventing a supersymmetric vacuum. Through a combination of field-theoretic techniques (F-term analysis, chiral ring structure, Konishi anomalies) and gravity-side arguments, the authors argue that SUSY is broken on the mesonic branch, with possible restrictions on baryonic branches and gravity solutions. They further suggest that SUSY-BOG is a general mechanism applicable to broader classes of CY singularities (e.g., Y^{p,q} with p>q, higher del Pezzos), offering a framework for controlled SUSY-breaking vacua in string theory.

Abstract

We conjecture a geometric criterion for determining whether supersymmetry is spontaneously broken in certain string backgrounds. These backgrounds contain wrapped branes at Calabi-Yau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a particular example: the $Y^{2,1}$ quiver gauge theory corresponding to a cone over the first del Pezzo surface, $dP_1$. This setup can be analyzed using ordinary supersymmetric field theory methods, where we find that gaugino condensation drives a deformation of the chiral ring which has no solutions. We expect this breaking to be a general feature of any theory of branes at a singularity with a smaller number of possible deformations than independent anomaly-free fractional branes.

Supersymmetry Breaking from a Calabi-Yau Singularity

TL;DR

The paper proposes a geometric criterion, SUSY-BOG, for spontaneous supersymmetry breaking in string backgrounds with Calabi-Yau singularities and wrapped branes, focusing on obstructions to complex structure deformations. It analyzes the cone over the first del Pezzo surface, dP1, via its dual gauge theory (Y^{2,1}) and shows that while gaugino condensation deforms the chiral ring, the deformation is obstructed, preventing a supersymmetric vacuum. Through a combination of field-theoretic techniques (F-term analysis, chiral ring structure, Konishi anomalies) and gravity-side arguments, the authors argue that SUSY is broken on the mesonic branch, with possible restrictions on baryonic branches and gravity solutions. They further suggest that SUSY-BOG is a general mechanism applicable to broader classes of CY singularities (e.g., Y^{p,q} with p>q, higher del Pezzos), offering a framework for controlled SUSY-breaking vacua in string theory.

Abstract

We conjecture a geometric criterion for determining whether supersymmetry is spontaneously broken in certain string backgrounds. These backgrounds contain wrapped branes at Calabi-Yau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a particular example: the quiver gauge theory corresponding to a cone over the first del Pezzo surface, . This setup can be analyzed using ordinary supersymmetric field theory methods, where we find that gaugino condensation drives a deformation of the chiral ring which has no solutions. We expect this breaking to be a general feature of any theory of branes at a singularity with a smaller number of possible deformations than independent anomaly-free fractional branes.

Paper Structure

This paper contains 17 sections, 77 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The Conifold vs. $dP_1$
  3. Summary of the $dP_1$ Argument
  4. The Gauge Theory for $dP_1$
  5. The Chiral Ring
  6. The First del Pezzo
  7. D5-branes and Superconformal Fixed Points
  8. The Quantum Moduli Space
  9. SUSY Breaking for Strongly Coupled $SU(3N)$
  10. Konishi Anomaly Equations
  11. The Baryonic Branch
  12. Outlook
  13. Relations for the first del Pezzo
  14. Gauge Theories and Chiral Rings for the $Y^{p,q}$
  15. Chiral Primaries for General $Y^{p,q}$
  16. ...and 2 more sections

Figures (4)

  • Figure 1: The quiver theory for $Y^{2,1}$, also known as an irregular $U(1)$ fibration of ${\mathbb P}^2$ blown up at a point.
  • Figure 2: The lattice points which generate the dual cone for ${\mathbb P}^2$ blown up at a point.
  • Figure 3: Shown are a) the unit cell $\sigma$; b) the unit cell $\tau$; and c) the quiver for $Y^{4,3}$, $\sigma \tilde{\tau} \sigma \tilde{\sigma}$.
  • Figure 4: The dual cone $\sigma^\vee$ for $Y^{5,1}$. The $a$ type operators correspond to lattice points along the red line, the $b$ type operators to lattice points along the green line, and the $c$ type operators to lattice points along the blue line.

Theorems & Definitions (1)

  • Conjecture