ModMax oscillators and root-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi><mml:mover accent="true"><mml:mi>T</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math>-like flows in supersymmetric quantum mechanics
Christian Ferko, Alisha Gupta
Abstract
We construct a deformation of any ($0+1$)-dimensional theory of $N$ bosons with $SO(N)$ symmetry which is driven by a function of conserved quantities that resembles the root-$T\overline{T}$ operator of (2D) quantum field theories. In the special case of $N=2$ bosons and a harmonic oscillator potential, the solution to the flow equation is the ModMax oscillator of 2209.06296. We argue that the deforming operator is related, in a particular special regime, to the dimensional reduction of the 2D root-$T\overline{T}$ operator on a spatial circle. It follows that the ModMax oscillator is a dimensional reduction of the 4D ModMax theory to quantum mechanics, justifying the name. We then show how to construct a manifestly supersymmetric extension of this root-$T\overline{T}$-like operator for any ($0+1$)-dimensional theory with $SO(N)$ symmetry and $\mathcal{N}=2$ supersymmetry by defining a flow equation directly in superspace.