Random field Ising model and Parisi-Sourlas supersymmetry. Part II. Renormalization group

Kaviraj, Apratim; Rychkov, Slava; Trevisani, Emilio

doi:10.1007/jhep03(2021)219

Cited by 22 publications

(118 citation statements)

References 99 publications

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“…This drastically reduces the number of interactions to consider: only operators in Cardy fields which can be written as a leader of an S n singlet interaction are of interest. The RG relevance or irrelevance of the leader determines the fate of the whole interaction [28].…”

Section: Dimensional Reductionmentioning

confidence: 99%

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The fate of Parisi-Sourlas supersymmetry in Random Field models

Kaviraj¹,

Rychkov²,

Trevisani³

2021

Preprint

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Section: Dimensional Reductionmentioning

confidence: 99%

“…We computed their perturbative one-loop dimensions for the φ 3 case [35], following the standard -expansion methodology [36, 37], while the φ 4 case was considered previously in [38]. The results (classical dimension plus one-loop correction) are:…”

Section: Dimensional Reductionmentioning

confidence: 99%

The fate of Parisi-Sourlas supersymmetry in Random Field models

Kaviraj¹,

Rychkov²,

Trevisani³

2021

Preprint

Self Cite

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“…To derive it, one uses the stationary condition (4) and we stress that the Jacobian and non-Jacobian contributions to the action (22) interfere. TR 1,2 imply, respectively,…”

Section: Time Reversal Without Grassmannmentioning

confidence: 99%

“…Such SUSYs, which mix physical and Grassmann fields, look surprising in a statistical mechanical context; yet, as other symmetries in physics, they turn out to be a powerful tool to study a variety of problems. These range from the dy-* vivien.lecomte@univ-grenoble-alpes.fr namics of spin glasses [14,15], disordered spin models [16], or heteropolymers [17], to finite-size effects in critical dynamics [18], localization [19], renormalization of the random-field Ising model [20][21][22], symmetries of Hamiltonian dynamics [23,24], and metastability in overdamped [25] and inertial [26] Langevin dynamics, with Witten's SUSY version of Morse theory [27]. SUSYs have methodological implications for renormalization [28] and the derivation of variational principles [29] or of the Parisi-Wu stochastic quantization [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Supersymmetries in nonequilibrium Langevin dynamics

et al. 2021

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Stochastic phenomena are often described by Langevin equations, which serve as a mesoscopic model for microscopic dynamics. It has been known since the work of Parisi and Sourlas that reversible (or equilibrium) dynamics present supersymmetries (SUSYs). These are revealed when the path-integral action is written as a function not only of the physical fields, but also of Grassmann fields representing a Jacobian arising from the noise distribution. SUSYs leave the action invariant upon a transformation of the fields that mixes the physical and the Grassmann ones. We show that contrary to common belief, it is possible to extend the known reversible construction to the case of arbitrary irreversible dynamics, for overdamped Langevin equations with additive white noise-provided their steady state is known. The construction is based on the fact that the Grassmann representation of the functional determinant is not unique, and can be chosen so as to present a generalization of the Parisi-Sourlas SUSY. We show how such SUSYs are related to time-reversal symmetries and allow one to derive modified fluctuation-dissipation relations valid in nonequilibrium. We give as a concrete example the results for the Kardar-Parisi-Zhang equation.

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“…Another example of blocks across dimensions was uncovered in the context of Parisi-Sourlas supersymmetry[39,40].…”

mentioning

confidence: 99%

Superconformal boundaries in 4 − ϵ dimensions

Liendo

Vliet

2021

J. High Energ. Phys.

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Boundaries in three-dimensional $$ \mathcal{N} $$ N = 2 superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining 2d boundary algebra exhibits $$ \mathcal{N} $$ N = (0, 2) or $$ \mathcal{N} $$ N = (1) supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $$ \mathcal{N} $$ N = (1) supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the ϵ-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a super-symmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.

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Random field Ising model and Parisi-Sourlas supersymmetry. Part II. Renormalization group

Cited by 22 publications

References 99 publications

The fate of Parisi-Sourlas supersymmetry in Random Field models

The fate of Parisi-Sourlas supersymmetry in Random Field models

Supersymmetries in nonequilibrium Langevin dynamics

Superconformal boundaries in 4 − ϵ dimensions

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