Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

New string vacua from twistor spaces

Alessandro Tomasiello

TL;DR

The paper constructs a new class of AdS4 vacua in type IIA string theory with internal twistor spaces CP^3 or the flag manifold, featuring non-Einstein, non-Kähler metrics and full moduli stabilization by fluxes without orientifolds. It uses a ten-dimensional SU(3) structure framework on Tw(M4) with a non-integrable almost complex structure and a squashing parameter to derive explicit geometric and flux data, then imposes flux quantization to obtain discrete vacua. The results demonstrate an infinite lattice of AdS4 solutions controlled by flux quanta and geometry, without relying on KK reductions, and suggest potential holographic duals and uplift scenarios. Overall, the work broadens the landscape of stabilized AdS4 vacua and provides a concrete, fully ten-dimensional construction method on twistor spaces, with avenues for extensions to include RR sources and holographic interpretations.

Abstract

We find a new family of AdS_4 vacua in IIA string theory. The internal space is topologically either the complex projective space CP^3 or the "flag manifold" SU(3)/(U(1)xU(1)), but the metric is in general neither Einstein nor Kaehler. All known moduli are stabilized by fluxes, without using quantum effects or orientifold planes. The analysis is completely ten--dimensional and does not rely on assumptions about Kaluza--Klein reduction.

New string vacua from twistor spaces

TL;DR

The paper constructs a new class of AdS4 vacua in type IIA string theory with internal twistor spaces CP^3 or the flag manifold, featuring non-Einstein, non-Kähler metrics and full moduli stabilization by fluxes without orientifolds. It uses a ten-dimensional SU(3) structure framework on Tw(M4) with a non-integrable almost complex structure and a squashing parameter to derive explicit geometric and flux data, then imposes flux quantization to obtain discrete vacua. The results demonstrate an infinite lattice of AdS4 solutions controlled by flux quanta and geometry, without relying on KK reductions, and suggest potential holographic duals and uplift scenarios. Overall, the work broadens the landscape of stabilized AdS4 vacua and provides a concrete, fully ten-dimensional construction method on twistor spaces, with avenues for extensions to include RR sources and holographic interpretations.

Abstract

We find a new family of AdS_4 vacua in IIA string theory. The internal space is topologically either the complex projective space CP^3 or the "flag manifold" SU(3)/(U(1)xU(1)), but the metric is in general neither Einstein nor Kaehler. All known moduli are stabilized by fluxes, without using quantum effects or orientifold planes. The analysis is completely ten--dimensional and does not rely on assumptions about Kaluza--Klein reduction.

Paper Structure

This paper contains 11 sections, 39 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Review of Anti--de Sitter vacua in type IIA
  3. Geometry of twistor spaces
  4. Topology
  5. Almost complex structures
  6. ${\rm SU}(3)$ structure
  7. Metric
  8. Finding vacua
  9. Supergravity
  10. Flux quantization
  11. Comments and possible extensions

Figures (1)

  • Figure 1: This sketch shows the allowed interval for $\sigma$ in (\ref{['eq:interval']}), along with the three special cases already used for string vacua before this paper. This is not a moduli space, because of flux quantization, as discussed in section \ref{['sub:quant']}. In the two extrema nilsson-popewatamura-2sorokin-tkach-volkov-11-10, the Romans mass vanishes (see (\ref{['eq:m']}) and (\ref{['eq:susy']})); the solution can hence be lifted to M--theory. The resulting seven--dimensional metric on $S^7$ is Einstein in both cases. The metric at $\sigma=2$ admits a Kähler structure, but supersymmetry uses another almost complex structure. The case $\sigma=1$ was used in behrndt-cveticbehrndt-cvetic2.