E-Thesis 825 views 215 downloads
Perturbative and semiclassical exploration of dualities / WILL ROBERTS
Swansea University Author: WILL ROBERTS
DOI (Published version): 10.23889/SUthesis.62921
Abstract
In this work we consider Abelian gauge fields defined on a (3 + 1)-dimensional bulk spacetime, which is allowed to interact with a matter CFT living on a plane boundary. This gives a family of boundary conformal field theories parameterized by the gauge coupling τ in the upper-half plane. Combining...
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Swansea
2023
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| Institution: | Swansea University |
| Degree level: | Doctoral |
| Degree name: | Ph.D |
| Supervisor: | Kumar, Prem |
| URI: | https://cronfa.swan.ac.uk/Record/cronfa62921 |
| Abstract: |
In this work we consider Abelian gauge fields defined on a (3 + 1)-dimensional bulk spacetime, which is allowed to interact with a matter CFT living on a plane boundary. This gives a family of boundary conformal field theories parameterized by the gauge coupling τ in the upper-half plane. Combining this with the recently discovered web of dualities connecting (2 + 1)-dimensional quantum field theories and SL(2, Z) duality in the bulk, one can perform powerful resummations in perturbation theory. We put this to work by considering a free scalar field theory on the boundary, which has a self-duality under τ → − 1 in this setup. Leveraging on this we compute the two-loop anomalous dimension of the mass-squared operator, which is then resummed by imposing the self-duality. Our result can then be extrapolated to τ = 1 which, after a bulk SL(2, Z) transformation, is then related to the 3d Gross-Neveu model by 3d bosonization. In particular this allows us to make a prediction for the anomalous dimension of the mass operator in the 3d Gross-Neveu model. |
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| Keywords: |
Quantum field theory, condensed matter, duality, boundary conformal field theory |
| College: |
Faculty of Science and Engineering |