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Worldsheet formulations of gauge theories and gravity

Michael Reisenberger
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Abstract

The evolution operator for states of gauge theories in the graph representation (closely related to the loop representation of Gambini and Trias, and Rovelli and Smolin) is formulated as a weighted sum over worldsheets interpolating between initial and final graphs. As examples, lattice $SU(2)$ BF and Yang-Mills theories are expressed as worldsheet theories, and (formal) worldsheet forms of several continuum $U(1)$ theories are given. It is argued that the world sheet framework should be ideal for representing GR, at least euclidean GR, in 4 dimensions, because it is adapted to both the 4-diffeomorphism invariance of GR, and the discreteness of 3-geometry found in the loop representation quantization of the theory. However, the weighting of worldsheets in GR has not yet been found.

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Michael Reisenberger. 1994-12-12. Worldsheet formulations of gauge theories and gravity. https://arxiv.org/abs/gr-qc/9412035

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