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arXiv · 2306.14575

ModMax Oscillators and Root-$T \overline{T}$-Like Flows in Supersymmetric Quantum Mechanics

Christian Ferko·Alisha Gupta
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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 arXiv: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.

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Christian Ferko, Alisha Gupta. 2023-06-26. ModMax Oscillators and Root-$T \overline{T}$-Like Flows in Supersymmetric Quantum Mechanics. https://doi.org/10.1103/physrevd.108.046013

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