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The GS Type IIB Superstring Action on AdS(3) X S(3) X T(4)

Igor Pesando

TL;DR

This work constructs the Green–Schwarz type IIB superstring action on $AdS_{3}\times S^{3}\times T^{4}$ by encoding the background in the superspace $AdS_{3|4}\otimes S_{3}\otimes T^{4}$ and fixing $\kappa$-symmetry with a supersolvable algebra. It derives the full background for spontaneous compactification, expresses the IIB fields as superspace quantities, and obtains a gauge-fixed action that clearly interpolates between NSNS and RR regimes, with the WZW term disappearing in the pure RR limit. The paper shows that the action remains conformal under the appropriate WZ constructions and provides alternative 6D pseudo-Majorana Weyl spinor formulations for RR backgrounds. Overall, it advances explicit quantization approaches for strings in RR AdS backgrounds and contributes to understanding AdS$_3$/CFT$_2$ via a concrete, κ-fixed worldsheet action.

Abstract

We describe the type IIB supergravity background on AdS_{3} x S_{3} x T^{4} using the potentials of AdS_{3|4} x S_{3} x T^{4} and we use the supersolvable algebra associated to AdS_{3|4} to compute the kappa gauge fixed type IIB string action. From the explicit form of the action we can clearly see how passing from pure NSNS backgrounds to pure RR backgrounds the WZW term disappears.

The GS Type IIB Superstring Action on AdS(3) X S(3) X T(4)

TL;DR

This work constructs the Green–Schwarz type IIB superstring action on by encoding the background in the superspace and fixing -symmetry with a supersolvable algebra. It derives the full background for spontaneous compactification, expresses the IIB fields as superspace quantities, and obtains a gauge-fixed action that clearly interpolates between NSNS and RR regimes, with the WZW term disappearing in the pure RR limit. The paper shows that the action remains conformal under the appropriate WZ constructions and provides alternative 6D pseudo-Majorana Weyl spinor formulations for RR backgrounds. Overall, it advances explicit quantization approaches for strings in RR AdS backgrounds and contributes to understanding AdS/CFT via a concrete, κ-fixed worldsheet action.

Abstract

We describe the type IIB supergravity background on AdS_{3} x S_{3} x T^{4} using the potentials of AdS_{3|4} x S_{3} x T^{4} and we use the supersolvable algebra associated to AdS_{3|4} to compute the kappa gauge fixed type IIB string action. From the explicit form of the action we can clearly see how passing from pure NSNS backgrounds to pure RR backgrounds the WZW term disappears.

Paper Structure

This paper contains 14 sections, 81 equations.

Table of Contents

  1. Introduction.
  2. The supergravitational background.
  3. The spontaneous compactification on $AdS_{3}\otimes S_{3}\otimes T^{4}$ .
  4. The Killing vectors.
  5. The type IIB fields as fields living on the superspace $AdS_{3|4}\otimes S_{3}\otimes T^{4}$.
  6. Fixing the $\kappa$ symmetry using the supersolvable and the $\kappa$ gauge fixed expression for the supergravity background fields.
  7. The action.
  8. Conventions.
  9. Decomposition $so(2,2)=so(1,3)\oplus so(1,3)$ and $AdS_{3}$ .
  10. The $SU(1,1|2,0)$ and $SU(1,1|0,2)$ Maurer-Cartan.
  11. Derivation of the supergravitational background.
  12. The GS superstring action on $AdS_{3}\otimes S_{3}\otimes T^{4}$ in first order formalism and its $\kappa$ symmetry.
  13. Fixing the $\kappa$ symmetry with the supersolvable projector.
  14. Another useful expression for the pure RR action.