[Paper Review] Superconformal Deformations and Space-Time Symmetries

Ioannis Giannakis|ArXiv.org|Feb 25, 1999

Geophysics and Sensor Technology3 citations

TL;DR

This paper presents a first-order deformation method for the superstring's stress-energy tensor and supercurrent by turning on NS-NS bosonic fields, while identifying challenges in incorporating spacetime fermions and R-R fields. It derives the gauge symmetries of massless spacetime fields, offering a systematic framework for understanding superconformal deformations and their implications for space-time symmetries in string theory.

ABSTRACT

In this paper we present a method of deforming to first order the stress-tensor and the supercurrent of the superstring corresponding to turning on NS-NS bosonic fields. Furthermore we discuss the difficulties associated with turning on spacetime fermions and R-R bosons. We also derive the gauge symmetries of the massless spacetime fields.

Motivation & Objective

• To develop a systematic method for deforming the superconformal algebra of the superstring via NS-NS background fields.
• To address the challenges in coupling spacetime fermions and R-R fields to the superconformal current algebra.
• To derive the gauge symmetries associated with massless spacetime fields arising from the deformation procedure.
• To clarify the role of superconformal symmetry in the emergence of space-time symmetries under background field deformations.

Proposed method

• The paper employs a first-order perturbative approach to deform the stress-tensor and supercurrent of the superstring in the presence of NS-NS background fields.
• It uses the operator product expansion (OPE) structure of the current algebra to analyze how deformations affect the superconformal symmetry algebra.
• The method involves computing the first-order corrections to the OPEs of the stress-energy tensor and supercurrent under the influence of NS-NS fields.
• It systematically identifies the conditions under which the deformed algebra preserves superconformal invariance.
• The analysis extends to the gauge symmetry structure of the resulting massless spacetime fields, derived from the transformation properties of the deformed currents.
• It highlights obstructions in coupling R-R fields and spacetime fermions due to inconsistencies in the OPE closure and anomaly structure.

Experimental results

Research questions

• RQ1 How can the superconformal algebra of the superstring be deformed at first order by NS-NS background fields?
• RQ2 What are the obstructions to consistently coupling spacetime fermions and R-R fields to the superconformal current algebra?
• RQ3 Which gauge symmetries of massless spacetime fields emerge from the deformed superconformal current algebra?
• RQ4 How do the deformed current OPEs relate to the underlying space-time symmetries in string theory?
• RQ5 What constraints arise from requiring closure of the OPE algebra when including fermionic and R-R fields?

Key findings

• The first-order deformation of the stress-tensor and supercurrent is consistently implemented for NS-NS background fields, preserving the superconformal algebra structure.
• The method successfully derives the gauge symmetries of the massless spacetime fields that arise from the deformed current algebra.
• Obstructions are identified in coupling spacetime fermions and R-R fields due to anomalies and non-closure of the OPE algebra.
• The analysis confirms that NS-NS fields are compatible with superconformal invariance at first order, while R-R and fermionic couplings require additional consistency conditions.
• The paper establishes a direct link between the deformed superconformal current algebra and the gauge symmetries of spacetime fields in the effective string theory.