SciPost Thesis Link
Title:  Supersymmetry and Irrelevant Deformations  
Author:  Christian Ferko  
As Contributor:  Christian Ferko  
Type:  Ph.D.  
Field:  Physics  
Specialties: 


Approach:  Theoretical  
URL:  https://knowledge.uchicago.edu/record/3403/files/Ferko_uchicago_0330D_16007.pdf  
Degree granting institution:  The University of Chicago  
Supervisor(s):  Savdeep Sethi  
Defense date:  20210726 
Abstract:
The $T \overline{T}$ operator provides a universal irrelevant deformation of twodimensional 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 fullfledged string theory, but which is nonetheless under some analytic control. On the other hand, supersymmetry is a beautiful extension of PoincarĂ© 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 ''supercurrentsquared'' operator, which is closely related to $T \overline{T}$, in any twodimensional 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 supercurrentsquared are related to superstring and brane actions, and some of these theories possess extra nonlinearly realized supersymmetries. Finally, we show that $T \overline{T}$ defines a new theory of both abelian and nonabelian gauge fields coupled to charged matter, which includes models compatible with maximal supersymmetry. In analogy with the DiracBornInfeld (DBI) theory, which defines a nonlinear extension of Maxwell electrodynamics, these models possess a critical value for the electric field.