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Title:  Supersymmetry and Irrelevant Deformations
Author:  Christian Ferko
As Contributor:   Christian Ferko
Type: Ph.D.
Field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical
Degree granting institution:  The University of Chicago
Supervisor(s): Savdeep Sethi
Defense date:  2021-07-26


The $T \overline{T}$ operator provides a universal irrelevant deformation of two-dimensional quantum field theories with remarkable properties, including connections to both string theory and holography beyond $\mathrm{AdS}$ spacetimes. In particular, it appears that a $T \overline{T}$-deformed theory is a kind of new structure, which is neither a local quantum field theory nor a full-fledged string theory, but which is nonetheless under some analytic control. On the other hand, supersymmetry is a beautiful extension of Poincaré symmetry which relates bosonic and fermionic degrees of freedom. The extra computational power provided by supersymmetry renders many calculations more tractable. It is natural to ask what one can learn about irrelevant deformations in supersymmetric quantum field theories. In this work, we describe a presentation of the $T \overline{T}$ deformation in manifestly supersymmetric settings. We define a ''supercurrent-squared'' operator, which is closely related to $T \overline{T}$, in any two-dimensional theory with $(0, 1)$, $(1, 1)$, or $(2, 2)$ supersymmetry. This deformation generates a flow equation for the superspace Lagrangian of the theory, which therefore makes the supersymmetry manifest. In certain examples, the deformed theories produced by supercurrent-squared are related to superstring and brane actions, and some of these theories possess extra non-linearly realized supersymmetries. Finally, we show that $T \overline{T}$ defines a new theory of both abelian and non-abelian gauge fields coupled to charged matter, which includes models compatible with maximal supersymmetry. In analogy with the Dirac-Born-Infeld (DBI) theory, which defines a non-linear extension of Maxwell electrodynamics, these models possess a critical value for the electric field.

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