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Superstrings on AdS_4 x CP^3 from Supergravity

Riccardo D'Auria, Pietro Fre', Pietro Antonio Grassi, Mario Trigiante

TL;DR

Problem: construct a BRST-invariant pure spinor description of strings on AdS4 × CP3 with RR flux. Approach: start from the type IIA FDA rheonomic formulation, implement a mini-superspace reduction to 24 fermionic coordinates, complete the gauge sector, and derive the explicit pure spinor action in the AdS4 × CP3 background. Contributions: explicit background tensor data (RR fields, dilaton, B^{[2]}, etc.), a background-adapted pure spinor constraint yielding 14 independent components, and a BRST-quantized action that matches the OSp(6|4) coset structure. Significance: provides a manifestly supersymmetric, RR-coupled worldsheet description suitable for analyzing integrability and α' corrections in the AdS4/CFT3 correspondence.

Abstract

We derive from a general formulation of pure spinor string theory on type IIA backgrounds the specific form of the action for the AdS_4 x P^3 background. We provide a complete geometrical characterization of the structure of the superfields involved in the action.

Superstrings on AdS_4 x CP^3 from Supergravity

TL;DR

Problem: construct a BRST-invariant pure spinor description of strings on AdS4 × CP3 with RR flux. Approach: start from the type IIA FDA rheonomic formulation, implement a mini-superspace reduction to 24 fermionic coordinates, complete the gauge sector, and derive the explicit pure spinor action in the AdS4 × CP3 background. Contributions: explicit background tensor data (RR fields, dilaton, B^{[2]}, etc.), a background-adapted pure spinor constraint yielding 14 independent components, and a BRST-quantized action that matches the OSp(6|4) coset structure. Significance: provides a manifestly supersymmetric, RR-coupled worldsheet description suitable for analyzing integrability and α' corrections in the AdS4/CFT3 correspondence.

Abstract

We derive from a general formulation of pure spinor string theory on type IIA backgrounds the specific form of the action for the AdS_4 x P^3 background. We provide a complete geometrical characterization of the structure of the superfields involved in the action.

Paper Structure

This paper contains 22 sections, 132 equations.

Table of Contents

  1. Introduction
  2. Summary of Type IIA Supergravity and of its FDA
  3. Definition of the curvatures
  4. Rheonomic parametrizations of the curvatures in the string frame
  5. Bosonic curvatures
  6. Fermionic curvatures
  7. Field equations of type IIA supergravity in the string frame
  8. Compactifications of type IIA on $\mathrm{AdS}_4 \, \times \, {\mathbb{P}}^3$
  9. Killing spinors of the $\mathrm{AdS_4}$ manifold
  10. Explicit construction of $\mathbb{P}^3$ geometry
  11. The compactification ansatz
  12. Killing spinors on $\mathbb{P}^3$
  13. Gauge completion in mini superspace
  14. Gauge completion of the $\mathbf{B}^{[2]}$ form
  15. Rewriting the mini-superspace gauge completion as MC forms on the complete supercoset
  16. ...and 7 more sections