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A fractal formulation of string on fractal curves
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DOI：10.1007/s40509-026-00388-9.png)
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Abstract
En 中文
In this paper, we propose a fractal formulation of string theory by extending the classical string framework to fractal geometries. We begin by developing the dynamics of fractal strings on fractal curves and derive the corresponding equations of motion in spaces characterized by non-integer dimensions. A fractal conformal gauge together with light-cone coordinates is then introduced, allowing a consistent simplification of the governing equations within the fractal setting. We further formulate fractal open and fractal closed strings, showing how fractal geometry modifies their dynamics and boundary conditions. These results indicate that the presence of fractal structures significantly influences string modes and their physical interpretation. The proposed framework provides a unified and self-consistent approach to string dynamics in fractal space-time and opens new directions for investigating quantization, symmetries, and potential physical applications of strings in fractal geometries.
Keywords:
String theory
Fractal geometry
Fractal curves
Conformal gauge
Light-cone coordinates
Open and closed strings
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