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Published:- October 2025

Abstract

Significant progress has been made in recent years on generalized global symmetries . In this paper, we provide a detailed and comprehensive discussion on topological operators , generalized global symmetries , higher -form symmetries with a concrete example using Maxwell’s $4D$ theory. We revisit the problem from the perspective of generalized and higher-form symmetries, focusing on the fate of their associated topological operators when they are embedded in gravity. Topological defects have been categorized as solitonic effects in a field profile with appropriate

regularization to derive a complete effective action for non-trivial Effective Field Theories(EFTs), which includes gravity. While studying topological operators, it is essential to take into consideration a perturbative regime within which EFTs can be constructed and topological invariance can also be preserved. Considering a $d$ dimensional EFT that is weakly coupled to Einstein gravity, we continue our investigation into the species scale. A lagrangian that includes the classical gravitation action coupled with matter fields has also been formalised. Taking into consideration the issues that occur with constructing consistent theories of Quantum Gravity in large moduli spaces , within the Planck scale, the paper briefly touches upon Swampland and Swampland Distance Conjecture(SDC)in order to analyse the nature of Goldstone sectors in large field spaces. Finally, we show how missing EFT degrees of freedom can be used to recover topological operators. For both dynamical/non-dynamical charges, we study symmetry-violations and the preservation of topological invariance at larger masses for heavier fields. A suppression factor has also been introduced to mitigate deviations at finite masses.

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Citation

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@misc{nandi_2025_17253407,
  author       = {Nandi, Soumyadip},
  title        = {Topological Operators in Quantum Gravity:- A
                   Treatment within Effective Field Theory
                   Consistency
                  },
  month        = oct,
  year         = 2025,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.17253407},
  url          = {https://doi.org/10.5281/zenodo.17253407},
}