Flows in the Space of Interacting Chiral Boson Theories
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| Format: | Preprint |
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2024
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| _version_ | 1866913459184074752 |
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| author | Ebert, Stephen Ferko, Christian Martin, Cian Luke Tartaglino-Mazzucchelli, Gabriele |
| author_facet | Ebert, Stephen Ferko, Christian Martin, Cian Luke Tartaglino-Mazzucchelli, Gabriele |
| contents | We study interacting theories of $N$ left-moving and $\overline{N}$ right-moving Floreanini-Jackiw bosons in two dimensions. A parameterized family of such theories is shown to enjoy (non-manifest) Lorentz invariance if and only if its Lagrangian obeys a flow equation driven by a function of the energy-momentum tensor. We discuss the canonical quantization of such theories along classical stress tensor flows, focusing on the case of the root-$T \overline{T}$ deformation, where we obtain perturbative results for the deformed spectrum in a certain large-momentum limit. In the special case $N = \overline{N}$, we consider the quantum effective action for the root-$T \overline{T}$-deformed theory by expanding around a general classical background, and we find that the one-loop contribution vanishes for backgrounds with constant scalar gradients. Our analysis can also be interpreted via dual $U(1)$ Chern-Simons theories in three dimensions, which might be used to describe deformations of charged $\mathrm{AdS}_3$ black holes or quantum Hall systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_18242 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Flows in the Space of Interacting Chiral Boson Theories Ebert, Stephen Ferko, Christian Martin, Cian Luke Tartaglino-Mazzucchelli, Gabriele High Energy Physics - Theory Strongly Correlated Electrons General Relativity and Quantum Cosmology Mathematical Physics We study interacting theories of $N$ left-moving and $\overline{N}$ right-moving Floreanini-Jackiw bosons in two dimensions. A parameterized family of such theories is shown to enjoy (non-manifest) Lorentz invariance if and only if its Lagrangian obeys a flow equation driven by a function of the energy-momentum tensor. We discuss the canonical quantization of such theories along classical stress tensor flows, focusing on the case of the root-$T \overline{T}$ deformation, where we obtain perturbative results for the deformed spectrum in a certain large-momentum limit. In the special case $N = \overline{N}$, we consider the quantum effective action for the root-$T \overline{T}$-deformed theory by expanding around a general classical background, and we find that the one-loop contribution vanishes for backgrounds with constant scalar gradients. Our analysis can also be interpreted via dual $U(1)$ Chern-Simons theories in three dimensions, which might be used to describe deformations of charged $\mathrm{AdS}_3$ black holes or quantum Hall systems. |
| title | Flows in the Space of Interacting Chiral Boson Theories |
| topic | High Energy Physics - Theory Strongly Correlated Electrons General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2403.18242 |