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String instanton in AdS(4)xCP(3)

Alessandra Cagnazzo, Dmitri Sorokin, Linus Wulff

TL;DR

This work analyzes a string instanton in the AdS$_4\times$CP$^3$ background, focusing on a worldsheet wrapping a nontrivial CP$^1$ inside CP$^3$. By reducing the Green–Schwarz action to quadratic order in fermions and performing a careful kappa-symmetry gauge fixing, the authors derive the fermionic equations of motion on the instanton and count the zero modes. They find exactly $12$ fermionic zero modes, split into eight massive and four massless-like modes, all tied to the background supersymmetries and the monopole structure on the worldsheet, establishing the instanton as 1/2 BPS. The results imply potential non-perturbative corrections to the worldsheet dynamics and offer a bridge to M-theory via the Euclidean M2-brane counterpart, with implications for ABJM/ABJ generalizations and the AdS$_4$/CFT$_3$ correspondence.

Abstract

We study the string instanton wrapping a non-trivial two-cycle in CP(3) of the type IIA string theory compactified on AdS_4 x CP(3) superspace and find that it has twelve fermionic zero modes associated with 1/2 of the supersymmetry of the background thus manifesting that this classical instanton configuration is 1/2 BPS

String instanton in AdS(4)xCP(3)

TL;DR

This work analyzes a string instanton in the AdSCP background, focusing on a worldsheet wrapping a nontrivial CP inside CP. By reducing the Green–Schwarz action to quadratic order in fermions and performing a careful kappa-symmetry gauge fixing, the authors derive the fermionic equations of motion on the instanton and count the zero modes. They find exactly fermionic zero modes, split into eight massive and four massless-like modes, all tied to the background supersymmetries and the monopole structure on the worldsheet, establishing the instanton as 1/2 BPS. The results imply potential non-perturbative corrections to the worldsheet dynamics and offer a bridge to M-theory via the Euclidean M2-brane counterpart, with implications for ABJM/ABJ generalizations and the AdS/CFT correspondence.

Abstract

We study the string instanton wrapping a non-trivial two-cycle in CP(3) of the type IIA string theory compactified on AdS_4 x CP(3) superspace and find that it has twelve fermionic zero modes associated with 1/2 of the supersymmetry of the background thus manifesting that this classical instanton configuration is 1/2 BPS

Paper Structure

This paper contains 18 sections, 111 equations.

Table of Contents

  1. Introduction
  2. $AdS_4\times CP^3$ superstring action up to the quadratic order in fermions
  3. String instanton wrapping a two--sphere inside $CP^3$
  4. Bosonic part of the instanton solution
  5. Fermionic equations of motion and the fermionic zero modes of the string instanton on $CP^3$
  6. Restriction to the instanton solution
  7. Fermionic zero modes and supersymmetry
  8. Summary and Discussion
  9. Appendix A. Main notation and conventions
  10. $AdS_4$ space
  11. $CP^3$ space
  12. Type IIA $AdS_4\times CP^3$ superspace
  13. Superspace constraints
  14. $24+8$ splitting of $32$ $\Theta$
  15. The explicit form of the geometry of the $AdS_4\times CP^3$ superspace
  16. ...and 3 more sections