Abstract
Two dimensional gauge theories with charged matter fields are useful toy models for studying gauge theory dynamics, and in particular for studying the duality of large N gauge theories to perturbative string theories. A useful starting point for such studies is the pure Yang-Mills theory, which is exactly solvable. Its 1/N expansion was interpreted as a string theory by Gross and Taylor 30 years ago, but they did not provide a worldsheet action for this string theory, and such an action is useful for coupling it to matter fields. The chiral sector of the Yang-Mills theory can be written as a sum over holomorphic maps and has useful worldsheet descriptions, but the full theory includes more general extremal-area maps; a formal worldsheet action including all these maps in a “topological rigid string theory” was written by Hořava many years ago, but various subtleties arise when trying to use it for computations. In this paper we suggest a Polyakov-like generalization of Hořava’s worldsheet action which is well-defined, and we show how it reproduces the free limit of the Yang-Mills theory, both by formal arguments and by explicitly computing its partition function in several cases. In the future we plan to generalize this string theory to the finite-coupling gauge theory, and to analyze it with boundaries, corresponding either to Wilson loops or to dynamical matter fields in the fundamental representation.
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Acknowledgments
We would like to thank Netanel Barel, Matthias Gaberdiel, David Gross, Shota Komatsu, David Kutasov, Ohad Mamroud, Joe Minahan, Erez Urbach, and Edward Witten for useful discussions. This work was supported in part by an Israel Science Foundation (ISF) center for excellence grant (grant number 2289/18), by ISF grant no. 2159/22, by Simons Foundation grant 994296 (Simons Collaboration on Confinement and QCD Strings), by grant no. 2018068 from the United States-Israel Binational Science Foundation (BSF), by the Minerva foundation with funding from the Federal German Ministry for Education and Research, by the German Research Foundation through a German-Israeli Project Cooperation (DIP) grant “Holography and the Swampland”, and by a research grant from Martin Eisenstein. OA is the Samuel Sebba Professorial Chair of Pure and Applied Physics.
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Aharony, O., Kundu, S. & Sheaffer, T. A string theory for two dimensional Yang-Mills theory. Part I. J. High Energ. Phys. 2024, 63 (2024). https://doi.org/10.1007/JHEP07(2024)063
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DOI: https://doi.org/10.1007/JHEP07(2024)063