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

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.

arXiv comment53 pages; LaTeX; v2: typos corrected, comments added; v3: published version

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Cited by in corpus (10)

• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• Quantization of the ModMax Oscillator
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• Flows in the Space of Interacting Chiral Boson Theories
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• Waves and strings in an interacting conformal chiral 2-form theory in six dimensions
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
• Accelerating electrically charged ModMax black hole solutions in $F(R)$ gravity