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Chirality Change in String Theory

M. R. Douglas, C-G. Zhou

TL;DR

The paper shows that string vacua with different chiral spectra can be connected by classical deformations, not only via nonperturbative phase transitions. It develops intuition through toy EFT models and then demonstrates, in heterotic and Type IIA orientifold contexts, explicit constructions where the chiral content changes as one moves along supersymmetric or non-supersymmetric paths; central is the realization that $c_3(V)$ is not a topological invariant in these settings and that the true gauge structure is an infinite loop group of maps from the internal space. The work provides both finite-character results (finiteness of possible $c_3$ values for fixed data) and concrete examples (monads on the quintic, D6-branes on $T^6/(\mathbb{Z}_2\times\mathbb{Z}_2)$) showing how different chiral generations can emerge without invoking a nontrivial energy barrier. These insights suggest a broader, potentially unified framework for organizing string vacua, with transitions occurring along supersymmetric moduli spaces in certain settings, though several questions about universality and full nonperturbative control remain.

Abstract

It is known that string theory compactifications leading to low energy effective theories with different chiral matter content ({\it e.g.} different numbers of standard model generations) are connected through phase transitions, described by non-trivial quantum fixed point theories. We point out that such compactifications are also connected on a purely classical level, through transitions that can be described using standard effective field theory. We illustrate this with examples, including some in which the transition proceeds entirely through supersymmetric configurations.

Chirality Change in String Theory

TL;DR

The paper shows that string vacua with different chiral spectra can be connected by classical deformations, not only via nonperturbative phase transitions. It develops intuition through toy EFT models and then demonstrates, in heterotic and Type IIA orientifold contexts, explicit constructions where the chiral content changes as one moves along supersymmetric or non-supersymmetric paths; central is the realization that is not a topological invariant in these settings and that the true gauge structure is an infinite loop group of maps from the internal space. The work provides both finite-character results (finiteness of possible values for fixed data) and concrete examples (monads on the quintic, D6-branes on ) showing how different chiral generations can emerge without invoking a nontrivial energy barrier. These insights suggest a broader, potentially unified framework for organizing string vacua, with transitions occurring along supersymmetric moduli spaces in certain settings, though several questions about universality and full nonperturbative control remain.

Abstract

It is known that string theory compactifications leading to low energy effective theories with different chiral matter content ({\it e.g.} different numbers of standard model generations) are connected through phase transitions, described by non-trivial quantum fixed point theories. We point out that such compactifications are also connected on a purely classical level, through transitions that can be described using standard effective field theory. We illustrate this with examples, including some in which the transition proceeds entirely through supersymmetric configurations.

Paper Structure

This paper contains 16 sections, 79 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Toy models
  3. Kaluza-Klein reduction on $S^1$
  4. Connections on $S^2$
  5. Fermion zero modes on $S^2$ and change of chirality
  6. What is going on
  7. The torus $T^2$ and the brane picture
  8. Holomorphic bundles, splitting type, and Yang-Mills connections
  9. Chirality change on compact Calabi-Yau in heterotic string theory
  10. Chirality from reducible connections
  11. Finiteness of the number of possible $c_3$'s
  12. Explicit search on the quintic
  13. Smooth chirality change in type IIA orientifold
  14. Type IIA orientifold compactification on $T^6/{\mathbb{Z}}_2\times{\mathbb{Z}}_2$
  15. Smooth brane deformation and supersymmetric chirality change
  16. ...and 1 more sections

Figures (2)

  • Figure 1: Two intersecting D8 branes deform to a configuration without intersection, which realizes the change of chirality change.
  • Figure 2: Two intersecting complex curves described by the equation $xy=0$ deform to a a configuration described by the equation $xy=\epsilon$. x and y are complex coordinates, so these are Riemann surfaces, and the one in the second picture is connected. It would be easier to visulize if one regards this as degree-2 curve defined in a coordinate patch specified by $z\neq 0$ in $P^2$ with homogeneous coordinates (x,y,z).