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Superpotentials From Stringy Instantons Without Orientifolds

Christoffer Petersson

Abstract

In this paper we show that it is possible to derive non-perturbative superpotential terms from a stringy instanton without introducing orientifold planes. The instanton is realized by a Euclidean D brane wrapping a non-trivial cycle upon which we also wrap a single space-filling D brane. The standard problem of unwanted neutral fermionic zero modes is evaded by the appearance of couplings to charged bosonic zero modes in the instanton moduli action. Since the Euclidean D brane wraps a cycle which is not associated to any low energy gauge dynamics, it can not be interpreted as an ordinary gauge instanton, but rather as a stringy one. By considering such a brane configuration at an orbifold singularity, we can explicitly evaluate the instanton moduli space integral and find a holomorphic superpotential term with the structure of a baryonic mass term.

Superpotentials From Stringy Instantons Without Orientifolds

Abstract

In this paper we show that it is possible to derive non-perturbative superpotential terms from a stringy instanton without introducing orientifold planes. The instanton is realized by a Euclidean D brane wrapping a non-trivial cycle upon which we also wrap a single space-filling D brane. The standard problem of unwanted neutral fermionic zero modes is evaded by the appearance of couplings to charged bosonic zero modes in the instanton moduli action. Since the Euclidean D brane wraps a cycle which is not associated to any low energy gauge dynamics, it can not be interpreted as an ordinary gauge instanton, but rather as a stringy one. By considering such a brane configuration at an orbifold singularity, we can explicitly evaluate the instanton moduli space integral and find a holomorphic superpotential term with the structure of a baryonic mass term.

Paper Structure

This paper contains 13 sections, 26 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. The Orbifold Projection of the $k=1$ Instanton Sector of $\mathcal{N}$=4 SYM
  3. The Gauge Sector
  4. The Neutral Sector
  5. The Charged Sector
  6. The Moduli Space Integral
  7. Determining the Prefactor
  8. The Gauge Instanton
  9. The Stringy Instanton
  10. Evaluating the Moduli Space Integral
  11. Fermionic Integration
  12. Bosonic Integration
  13. Implications for the Gauge Dynamics

Figures (1)

  • Figure 1: The $\mathbb{Z}_2 \times \mathbb{Z}_2$ orbifold quiver gauge theory where the fractional D3 branes (green circles) have been given rank assignment ($N_1$,$N_2$,$N_3$,0). We have also included all neutral and charged zero modes of the fractional instanton (red square) which is located at node 3, together with $N_3$ fractional D3 branes.