A Loop Quantum Gravity Inspired Action for the Bosonic String and Emergent Dimensions at Large Scales

TL;DR

The paper addresses integrating loop quantum gravity's minimum area quanta with bosonic string dynamics by introducing a minimum worldsheet area Δ and a small coupling k = l_{pl}/l_s into the Nambu–Goto action. It develops a bimetric string framework and an inverse-metric Polyakov formulation, connecting area corrections to the Kalb–Ramond pullback and revealing Born–Infeld-like structure; it further constructs a holographic, connection-based string action with an emergent scale direction by gauging ISO(D+1,1) on the worldsheet. Upon covariant quantization, the model yields an anomaly-free Virasoro–Klein–Gordon-like algebra with a truncated, dimension-agnostic spectrum and no negative-norm ghosts, while admitting spin-1 and spin-2 background excitations tied to G_{μν}, B_{μν}, and Φ. The framework also aligns with Afshordi’s emergent dimensions, constraining dispersion relations and suggesting a Planck-scale effective (2+1)-dimensional gravity sector, with a holographic interpretation that ties bulk geometry to worldsheet gauge structure. Overall, the work provides a concrete, background-independent avenue to blend LQG geometry with string dynamics, opening paths to holographic descriptions and cosmological implications at large scales.

Abstract

We propose a modification of the Nambu-Goto action for the bosonic string which is compatible with the existence of a minimum area at the Planck scale. The result is a phenomenological action based on the observation that LQG tells us that areas of two-surfaces are operators in quantum geometry and are bounded from below. This leads us to a string action which is similar to that of bimetric gravity. We provide formulations of the bimetric string action for both the Nambu-Goto (second order) and Polyakov (first order) formulations. We explore the classical solutions of this action and its quantization and relate it to the conventional string solutions. We further construct a string action in which the effect of the background geometry is described in terms of the pullback of the bulk connection, which encodes the bulk geometry, to the worldsheet. The resulting string action is in the form of a gauged sigma model, where the spacetime co-ordinates are now vectors which transform under the Poincaré group $ISO(D,1)$. This requires the introduction of an auxiliary bulk co-ordinate which has a natural interpretation as a holographic or scale direction. We discuss possible cosmological implications of such a large scale emergent dimension.