Spectral Fractional Bosonic Strings: Exact Polyakov Measure and the Critical Dimension
Abstract
Fractional Laplacians encode anomalous scaling and covariant nonlocal response in quantum matter and holographic boundary systems. We place the corresponding scalar spectral theory on a dynamical closed worldsheet. A metric-dependent intertwiner maps the fractional quadratic form to that of D free bosons, while its zeta Jacobian changes the matter determinant weight from D to sD. The prime-determinant transformation includes the zero-mode area factor and determines both the moduli density and the Weyl coefficient cdet=sD. Weyl cancellation therefore selects D∗=26/s. On the integer critical locus 1≤ D≤26, N=26−D spectator bosons turn the residual determinant into a local critical CFT. Its fixed-area genus-g vacuum measure is that of 26 free bosons, its torus trace is modular invariant, its plumbing channels are state resolved, and its BRST charge is nilpotent. The D distinguished coordinates remain spectral composites; their pullback yields the Koba--Nielsen amplitudes and massless vertex conditions. Target backgrounds coupled to this distinguished sector retain the ordinary one-loop tensor beta functions, with dilaton deficit sD−26 and the corresponding string-frame action. Worldsheet gravity thus turns the fractional exponent into a quantum-geometric consistency parameter.
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BibTeX
@misc{wu2026spectral,
title = {{Spectral Fractional Bosonic Strings: Exact Polyakov Measure and the Critical Dimension}},
author = {Tianhao Wu and Gabriele La Nave},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27873},
eprint = {2609.27873},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27873},
}
RIS
TY - UNPB
TI - Spectral Fractional Bosonic Strings: Exact Polyakov Measure and the Critical Dimension
AU - Tianhao Wu
AU - Gabriele La Nave
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27873
UR - https://arxiv.org/abs/2609.27873
AB - Fractional Laplacians encode anomalous scaling and covariant nonlocal response in quantum matter and holographic boundary systems. We place the corresponding scalar spectral theory on a dynamical closed worldsheet. A metric-dependent intertwiner maps the fractional quadratic form to that of D free bosons, while its zeta Jacobian changes the matter determinant weight from D to sD. The prime-determinant transformation includes the zero-mode area factor and determines both the moduli density and the Weyl coefficient c_det=sD. Weyl cancellation therefore selects D_∗=26/s. On the integer critical locus 1≤ D≤26, N=26−D spectator bosons turn the residual determinant into a local critical CFT. Its fixed-area genus-g vacuum measure is that of 26 free bosons, its torus trace is modular invariant, its plumbing channels are state resolved, and its BRST charge is nilpotent. The D distinguished coordinates remain spectral composites; their pullback yields the Koba--Nielsen amplitudes and massless vertex conditions. Target backgrounds coupled to this distinguished sector retain the ordinary one-loop tensor beta functions, with dilaton deficit sD−26 and the corresponding string-frame action. Worldsheet gravity thus turns the fractional exponent into a quantum-geometric consistency parameter.
ER -