Abstract
We argue that String Theory and Loop Quantum Gravity can be thought of as describing different regimes of a single unified theory of quantum gravity. LQG can be thought of as providing the pre-geometric exoskeleton out of which macroscopic geometry emerges and String Theory then becomes the effective theory which describes the dynamics of that exoskeleton. The core of the argument rests on the claim that the Nambu-Goto action of String Theory can be viewed as the expectation value of the LQG area operator evaluated on the string worldsheet. A concrete result is that the string tension of String Theory and the Barbero-Immirzi parameter of LQG turn out to be proportional to each other.
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Notes
- 1.
Though note [18, 19] where disagreements between the two sets of calculations are pointed out. Though certain factors are not the same, the overall form of the entropy area relation including logarithmic corrections is the same. The differences could possibly be traced to the use of Euclidean geometry to determine black hole entropy in string theory. This introduces ingredients which are missing in the LQG calculation.
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- 3.
Though not all such geometries will be stable against perturbations. The formalism of Causal Dynamical Triangulations (CDT), closely related in spirit to LQG allows one to study this question in detail [1].
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Acknowledgements
The author would like to dedicate this article to his wife on the occasion of her birthday. The author wishes to acknowledge the support of a visiting associate fellowship from the Inter-University Centre For Astronomy And Astrophysics (IUCAA), Pune, India, where a portion of this work was completed.
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Vaid, D. (2021). Connecting Loop Quantum Gravity and String Theory via Quantum Geometry. In: Behera, P.K., Bhatnagar, V., Shukla, P., Sinha, R. (eds) XXIII DAE High Energy Physics Symposium. DAEBRNS HEPS 2018 2018. Springer Proceedings in Physics, vol 261. Springer, Singapore. https://doi.org/10.1007/978-981-33-4408-2_55
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