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Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
by Christian Ferko, Liam Smith, Gabriele Tartaglino-Mazzucchelli
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Christian Ferko |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2301.10411v3 (pdf) |
| Date accepted: | 2023-11-06 |
| Date submitted: | 2023-10-09 03:24 |
| Submitted by: | Ferko, Christian |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We identify the unique stress tensor deformation which preserves zero-birefringence conditions in non-linear electrodynamics, which is a $4d$ version of the ${T\overline{T}}$ operator. We study the flows driven by this operator in the three Lagrangian theories without birefringence -- Born-Infeld, Plebanski, and reverse Born-Infeld -- all of which admit ModMax-like generalizations using a root-${T\overline{T}}$-like flow that we analyse in our paper. We demonstrate one way of making this root-${T\overline{T}}$-like flow manifestly supersymmetric by writing the deforming operator in $\mathcal{N} = 1$ superspace and exhibit two examples of superspace flows. We present scalar analogues in $d = 2$ with similar properties as these theories of electrodynamics in $d = 4$. Surprisingly, the Plebanski-type theories are fixed points of the classical ${T\overline{T}}$-like flows, while the Born-Infeld-type examples satisfy new flow equations driven by relevant operators constructed from the stress tensor. Finally, we prove that any theory obtained from a classical stress-tensor-squared deformation of a conformal field theory gives rise to a related ``subtracted'' theory for which the stress-tensor-squared operator is a constant.
Author comments upon resubmission
List of changes
(1) Added a discussion around equation (2.20), and a sentence in the paragraph following equation (3.15), to clarify that the trace flow equation does not uniquely identify the operator driving a flow because it is indeterminate as $\lambda \to 0$, and is thus less fundamental.
(2) Extended the remarks in section 5.2, in particular between equations (5.15) and (5.19), to explain that the on-shell conditions which we use to analyze the root-$T^2$ flow are equivalent to using only the equation of motion for the auxiliary field.
(3) Added comments at the beginning of subsection 3.1, and after equation (3.73), to remind the reader that our results hold only for classical deformations of the Lagrangian.
(4) Clarified that the checks that the $T^2$ deformation preserves the zero birefringence condition, and that any stress tensor deformation preserves duality invariance, were only performed to first order in the deformation parameter.
Published as SciPost Phys. 15, 198 (2023)