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

TL;DR

This paper provides evidence for a non-trivial fixed point in the two-dimensional AdS non-linear sigma model, which could have implications for string theory and holography, based on multi-loop and large D calculations.

Contribution

It demonstrates the existence of a fixed point in AdS_{D+1} sigma models through four-loop and large D analyses, a novel insight into non-linear sigma models with AdS target spaces.

Findings

Evidence of a fixed point from four-loop calculations.

Large D analysis supports the fixed point existence.

Potential implications for holography and string vacua.

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(\alpha'^3) in the spacetime effective action) and on large D calculations carried to O(D^{-2}) (but to all orders in \alpha'). 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.