Solving the 2D SUSY Gross-Neveu-Yukawa model with conformal truncation

• Published in: The journal of high energy physics Vol. 2021; no. 1; pp. 1 - 42
• Main Authors: Fitzpatrick, A. Liam, Katz, Emanuel, Walters, Matthew T., Xin, Yuan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2021; Springer Nature B.V; Springer Nature; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Conformal Field Theory; Critical point; Elementary Particles; High energy physics; Ising model; Nonperturbative Effects; Operators (mathematics); Phase diagrams; Phase transitions; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetry; Symmetry; Two dimensional flow; Two dimensional models; Conformal Field Theory; Nonperturbative Effects
• DOI: 10.1007/JHEP01(2021)182
• ISSN: 1029-8479

A bstract We use Lightcone Conformal Truncation to analyze the RG flow of the two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a real scalar superfield with a ℤ 2 -symmetric cubic superpotential, aka the 2d Wess-Zumino model. The theory depends on a single dimensionless coupling g ¯ , and is expected to have a critical point at a tuned value g ¯ ∗ where it flows in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks the ℤ 2 symmetry on one side of this phase transition, and breaks SUSY on the other side. We calculate the spectrum of energies as a function of g ¯ and see the gap close as the critical point is approached, and numerically read off the critical exponent ν in TIM. Beyond the critical point, the gap remains nearly zero, in agreement with the expectation of a massless Goldstino. We also study spectral functions of local operators on both sides of the phase transition and compare to analytic predictions where possible. In particular, we use the Zamolodchikov C -function to map the entire phase diagram of the theory. Crucial to this analysis is the fact that our truncation is able to preserve supersymmetry sufficiently to avoid any additional fine tuning.