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Emergent SUSY in two dimensions

Ken Kikuchi

TL;DR

The paper demonstrates a two-dimensional renormalization-group flow in which supersymmetry emerges in the infrared from a non-Lagrangian UV theory. It combines symmetry-based constraints from topological defect lines with a new spin-content bound and nonperturbative truncation-space numerics to steer the flow from the fermionic $m=5$ minimal model to the fermionic $m=4$ minimal model endowed with ${\mathcal N}=1$ SUSY, including an emergent ${\mathbb Z}_2\times{\mathbb Z}_2$ R-symmetry. Numerical evidence with the truncated conformal space approach yields an IR central charge $c_{\mathrm{IR}}\approx0.717383$ and half-integer-spin excitations consistent with the SUSY spectrum, while opposite sign deformations lead to a degenerate GSD indicative of a TQFT phase. The methods provide a non-Lagrangian, nonperturbative framework to realize SUSY in 2D and may generalize to other fermionic minimal models and RG flows.

Abstract

We propose a renormalization group flow with emergent supersymmetry in two dimensions from a non-Lagrangian theory. The ultraviolet theory does not have supersymmetry while the infrared theory does. We constrain the flow both analytically and numerically (truncated conformal space approach). Analytic constraints include a new spin constraint.

Emergent SUSY in two dimensions

TL;DR

The paper demonstrates a two-dimensional renormalization-group flow in which supersymmetry emerges in the infrared from a non-Lagrangian UV theory. It combines symmetry-based constraints from topological defect lines with a new spin-content bound and nonperturbative truncation-space numerics to steer the flow from the fermionic minimal model to the fermionic minimal model endowed with SUSY, including an emergent R-symmetry. Numerical evidence with the truncated conformal space approach yields an IR central charge and half-integer-spin excitations consistent with the SUSY spectrum, while opposite sign deformations lead to a degenerate GSD indicative of a TQFT phase. The methods provide a non-Lagrangian, nonperturbative framework to realize SUSY in 2D and may generalize to other fermionic minimal models and RG flows.

Abstract

We propose a renormalization group flow with emergent supersymmetry in two dimensions from a non-Lagrangian theory. The ultraviolet theory does not have supersymmetry while the infrared theory does. We constrain the flow both analytically and numerically (truncated conformal space approach). Analytic constraints include a new spin constraint.
Paper Structure (12 sections, 31 equations, 7 figures, 1 table)

This paper contains 12 sections, 31 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Constraining RG flows
  3. Application: an RG flow with emergent SUSY
  4. Analytic constraints
  5. Numerical study
  6. Discussion
  7. TDLs in fermionic $m=3,4,5$ minimal models
  8. $m=3$
  9. $m=4$
  10. $m=5$
  11. The other two RG flows
  12. RG flow from fermionic $m=4$ to $m=3$

Figures (7)

  • Figure 1: TCSA results: The spectra in the spin-zero sector for (a) positive and (b) negative relevant coupling $\lambda_{1,3}$. (c) fits the ground state energy with ansatz $1/R+R$: the actual spectrum (dotted blue) and the fitting (solid orange). A fitting region is chosen to get the best fit. (d) shows the spectra in the spin 3/2 sector for $\lambda_{1,3}=+0.1$.
  • Figure 6: $\lambda_{2,1}=+0.1$
  • Figure 7: $\lambda_{2,1}=-0.1$
  • Figure 9: $\lambda_{3,3}=+0.1$
  • Figure 10: $\lambda_{3,3}=-0.1$
  • ...and 2 more figures