[Paper Review] Gauge fields-strings duality and tensionless superstrings

George Savvidy|ArXiv.org|Apr 17, 2003

Black Holes and Theoretical Physics5 references3 citations

TL;DR

This paper proposes a tensionless superstring theory using a perimeter action based on the extrinsic curvature of the worldsheet, which naturally leads to a vanishing string tension and a dual description of weakly coupled gauge theories. The model exhibits enhanced symmetries, including fermionic and BRST-like symmetries, and reduces to a topological field theory with vanishing central charge, offering a new framework for understanding the tensionless limit in string theory and its connection to high-spin gauge fields in AdS space.

ABSTRACT

The duality map between gauge theories and strings suggests that when the gauge theory is in the weak coupling regime the dual string tension effectively tends to zero, $α' o \infty$. This observation of Sundborg and Witten initiates a fresh interest to the old problem of tensionless limit of standard string theory and to the description of its genuine symmetries. We approach this problem formulating tensionless string theory by means of geometrical concept of surface perimeter. The perimeter action uniquely leads to a tensionless string theory.

Motivation & Objective

• To formulate a tensionless string theory that emerges in the weak-coupling limit of gauge theories, where string tension T → 0.
• To establish a duality between gauge theories and strings by constructing a geometric action based on surface perimeter rather than area.
• To explore the genuine symmetries of tensionless strings, particularly fermionic and BRST-like symmetries, in the context of high-spin gauge field theories.
• To show that the model reduces to a topological field theory with vanishing central charge, indicating a symmetric phase of string theory.

Proposed method

• Formulates the tensionless string action as S = m ∫ d²ζ √h √(K^{ia}_a K^{ib}_b), where K is the second fundamental form, leading to a perimeter-dependent dynamics instead of area-dependent.
• Introduces an equivalent form S = (m/π) ∫ d²ζ √((Δ(h)X_μ)²), where Δ(h) is the Laplace-Beltrami operator on the worldsheet.
• Considers model B with independent worldsheet metric h_{ab} and embedding fields X^μ, breaking the standard relation h_{ab} = ∂_a X_μ ∂_b X_μ.
• Fixes the conformal gauge h_{ab} = ρ η_{ab} to derive an equivalent first-order action involving conjugate momenta Π^μ and auxiliary fields.
• Identifies two fermionic symmetries δ and δ̄, which are nilpotent and close to BRST-like transformations, with algebra δ² = δ̄² = 0 and {δ, δ̄} = 0.
• Shows that the energy-momentum tensor T_{++} and T_{--} are BRST commutators, implying the theory is topological with vanishing central charge.

Experimental results

Research questions

• RQ1 How can a tensionless string theory be consistently formulated using geometric invariants like the perimeter of the worldsheet?
• RQ2 What are the fundamental symmetries of the tensionless limit, and how do they relate to BRST and high-spin gauge symmetries?
• RQ3 How does the perimeter action lead to a reduction to a point-particle path integral in the degenerate limit?
• RQ4 What is the role of the Laplace-Beltrami operator Δ(h) in defining the tensionless action and its equivalence to the extrinsic curvature form?
• RQ5 Why does the energy-momentum tensor become a BRST commutator, and what does this imply for the quantum structure of the theory?

Key findings

• The perimeter action S = m ∫ d²ζ √h √(K^{ia}_a K^{ib}_b) uniquely leads to a tensionless string theory with vanishing string tension T = 1/(2πα') → 0.
• In the degenerate limit where the worldsheet collapses to a worldline, the action reduces to the relativistic point-particle action, extending the Feynman path integral to strings.
• The action is equivalent to S = (m/π) ∫ d²ζ √((Δ(h)X_μ)²), establishing a direct link between the extrinsic curvature and the Laplacian on the worldsheet.
• The model exhibits two nilpotent fermionic symmetries δ and δ̄, which close into a BRST-like algebra, indicating a topological structure.
• The energy-momentum tensor T_{++} and T_{--} are expressed as BRST commutators T_{++} = {Q_+, G_+}, implying the theory is topological with vanishing central charge.
• The supercurrent Q and U(1) current J_a are related via δJ_+ = -ε_- Q_+, showing that the supercurrent is a variation of the U(1) current under the fermionic symmetry.