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$T \overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry

by Christian Ferko, Yangrui Hu, Zejun Huang, Konstantinos Koutrolikos, Gabriele Tartaglino-Mazzucchelli

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Submission summary

Authors (as registered SciPost users): Christian Ferko
Submission information
Preprint Link:  (pdf)
Date accepted: 2024-01-11
Date submitted: 2023-12-14 02:58
Submitted by: Ferko, Christian
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We show that the $3d$ Born-Infeld theory can be generated via an irrelevant deformation of the free Maxwell theory. The deforming operator is constructed from the energy-momentum tensor and includes a novel non-analytic contribution that resembles root-$T \overline{T}$. We find that a similar operator deforms a free scalar into the scalar sector of the Dirac-Born-Infeld action, which describes transverse fluctuations of a D-brane, in any dimension. We also analyse trace flow equations and obtain flows for subtracted models driven by a relevant operator. In $3d$, the irrelevant deformation can be made manifestly supersymmetric by presenting the flow equation in $\mathcal{N} = 1$ superspace, where the deforming operator is built from supercurrents. We demonstrate that two supersymmetric presentations of the D2-brane effective action, the Maxwell-Goldstone multiplet and the tensor-Goldstone multiplet, satisfy superspace flow equations driven by this supercurrent combination. To do this, we derive expressions for the supercurrents in general classes of vector and tensor/scalar models by directly solving the superspace conservation equations and also by coupling to $\mathcal{N} = 1$ supergravity. As both of these multiplets exhibit a second, spontaneously broken supersymmetry, this analysis provides further evidence for a connection between current-squared deformations and nonlinearly realized symmetries.

Author comments upon resubmission

Attached is a revised version of our manuscript which incorporates the suggested changes which we received in the refereeing round.

List of changes

(1) We have added a sentence in the paragraph following equation (2.11) to clarify that we have made a sign choice which is appropriate for deforming field configurations with $\mathfrak{t} < 0$, but that one could have defined a piecewise deformation which works for all $\mathfrak{t}$.

(2) We added two paragraphs, at the bottom of page 18 and top of page 19, explaining the relationship between our results and those of 2308.12189.

(3) We clarified the discussion around equation (2.19) to better explain the role of possible total derivative terms, which are important for the later observations around equation (2.58).

(4) We corrected a typo in equation (2.34).

Published as SciPost Phys. 16, 038 (2024)

Reports on this Submission

Anonymous Report 2 on 2024-1-1 (Invited Report)


The authors have addressed my comments and therefore I am happy to recommend the article for publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2023-12-20 (Invited Report)


I would like to recommend the paper for publication and thank the authors for addressing all of my remarks.

  • validity: high
  • significance: good
  • originality: good
  • clarity: high
  • formatting: excellent
  • grammar: perfect

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