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A k Gauge Fixed Type IIB Superstring Action on AdS_{5} X S_{5}

I. Pesando

TL;DR

This work develops a κ-gauge fixed Type IIB superstring action on AdS$_{5}\times S_{5}$ by leveraging a supersolvable algebra to project half of the fermionic coordinates. The construction proceeds by (i) determining the IIB superbackground, (ii) rewriting it in terms of $AdS_{5|4}\otimes S_{5}$ generalized potentials, and (iii) fixing κ-symmetry via the supersolvable algebra, followed by inserting the results into the GHMNT first-order action. A key outcome is an explicit κ-fixed expression for the surviving $AdS_{5|4}$ potentials and a non-linear worldsheet action on AdS$_{5}\times S_{5}$, paving the way toward computing string amplitudes in this background. The approach clarifies the role of the solvable-algebra gauge in κ-symmetry fixing and highlights limitations in describing all string excitations within this gauge, while suggesting a pathway to quantization or reformulation for practical calculations.

Abstract

We describe the type IIB supergravity background on AdS_{5} X S_{5} using the potentials of AdS_{5|4} X S_{5} and we use the supersolvable algebra associated to AdS_{5|4} to compute the k gauge fixed type IIB string action.

A k Gauge Fixed Type IIB Superstring Action on AdS_{5} X S_{5}

TL;DR

This work develops a κ-gauge fixed Type IIB superstring action on AdS by leveraging a supersolvable algebra to project half of the fermionic coordinates. The construction proceeds by (i) determining the IIB superbackground, (ii) rewriting it in terms of generalized potentials, and (iii) fixing κ-symmetry via the supersolvable algebra, followed by inserting the results into the GHMNT first-order action. A key outcome is an explicit κ-fixed expression for the surviving potentials and a non-linear worldsheet action on AdS, paving the way toward computing string amplitudes in this background. The approach clarifies the role of the solvable-algebra gauge in κ-symmetry fixing and highlights limitations in describing all string excitations within this gauge, while suggesting a pathway to quantization or reformulation for practical calculations.

Abstract

We describe the type IIB supergravity background on AdS_{5} X S_{5} using the potentials of AdS_{5|4} X S_{5} and we use the supersolvable algebra associated to AdS_{5|4} to compute the k gauge fixed type IIB string action.

Paper Structure

This paper contains 8 sections, 26 equations.

Table of Contents

  1. Introduction.
  2. Step 1: determining the superbackground.
  3. Step 2: expressing the superbackground through the $AdS_{5|4}\bigotimes S_{5}$ generalized potentials.
  4. Step 3: fixing the $\kappa$ symmetry using the supersolvable algebra.
  5. The action.
  6. Conventions.
  7. The superstring action on $AdS_{5}\bigotimes S_{5}$ in first order formalism and its $\kappa$ symmetry.
  8. How the supersolvable algebra fixes the $\kappa$ symmetry.