Non-linear sigma models with anti-de Sitter target spaces

Abstract

We present evidence that there is a non-trivial fixed point for the AdS_{D+1} non-linear sigma model in two dimensions, without any matter fields or additional couplings beyond the standard quadratic action subject to a quadratic constraint. A zero of the beta function, both in the bosonic and supersymmetric cases, appears to arise from competition between one-loop and higher loop effects. A string vacuum based on such a fixed point would have string scale curvature. The evidence presented is based on fixed-order calculations carried to four loops (corresponding to O(α'^3) in the spacetime effective action) and on large D calculations carried to O(D^{-2}) (but to all orders in α'). We discuss ways in which the evidence might be misleading, and we discuss some features of the putative fixed point, including the central charge and an operator of negative dimension. We speculate that an approximately AdS_5 version of this construction may provide a holographic dual for pure Yang-Mills theory, and that quotients of an AdS_3 version might stand in for Calabi-Yau manifolds in compactifications to four dimensions.

44 pages, 4 figures. v2: references added

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Cited by in corpus (14)

• Strong-coupling expansion of cusp anomaly from quantum superstring
• Mimicking Lambda with a spin-two ghost condensate
• The Large D Limit of Einstein's Equations
• Continuum limit of fishnet graphs and AdS sigma model
• Toward a 3d Ising model with a weakly-coupled string theory dual
• Heterotic non-linear sigma models with anti-de Sitter target spaces
• Investigating Off-shell Stability of Anti-de Sitter Space in String Theory
• The heterotic string at high temperature (or with strong supersymmetry breaking)
• Sigma model on a squashed sphere with a Wess-Zumino term
• Bubble-resummation and critical-point methods for $\beta$-functions at large $N$
• First Order Semiclassical Thermal String in the AdS Spacetime
• The curious case of large-N expansions on a (pseudo)sphere
• Perturbative and nonperturbative correspondences between compact and non-compact sigma-models
• Nonlinear Sigma Models with Compact Hyperbolic Target Spaces