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Register a new userFive loop renormalization of the Wess-Zumino model
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J.A. Gracey
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We renormalize the Wess-Zumino model at five loops in both the minimal subtraction (MSbar) and momentum subtraction (MOM) schemes. The calculation is carried out automatically using a routine that performs the D-algebra. Generalizations of the model to include $O(N)$ symmetry as well as the case with real and complex tensor couplings are also considered. We confirm that the emergent SU(3) symmetry of six dimensional O(N) phi^3 theory is also a property of the tensor O(N) model. With the new loop order precision we compute critical exponents in the epsilon expansion for several of these generalizations as well as the XYZ model in order to compare with conformal bootstrap estimates in three dimensions. For example at five loops our estimate for the correction to scaling exponent is in very good agreement for the Wess-Zumino model which equates to the emergent supersymmetric fixed point of the Gross-Neveu-Yukawa model. We also compute the rational number that is part of the six loop MSbar beta-function.
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We consider a Galilean N=2 supersymmetric theory in 2+1 dimensions with F-term couplings, obtained by null reduction of a relativistic Wess-Zumino model. We compute quantum corrections and we check that, as for the relativistic parent theory, the F-term does not receive quantum corrections. Even more, we find evidence that the causal structure of the non-relativistic dynamics together with particle number conservation constrain the theory to be one-loop exact.
We revisit various topological issues concerning four-dimensional ungauged and gauged Wess-Zumino-Witten (WZW) terms for $SU$ and $SO$ quantum chromodynamics (QCD), from the modern bordism point of view. We explain, for example, why the definition of the $4d$ WZW terms requires the spin structure. We also discuss how the mixed anomaly involving the 1-form symmetry of $SO$ QCD is reproduced in the low-energy sigma model.
We investigate the breakdown of supersymmetry at finite temperature. While it has been proven that temperature always breaks supersymmetry, the nature of this breaking is less clear. On the one hand, a study of the Ward-Takahashi identities suggests a spontaneous breakdown of supersymmetry without the existence of a Goldstino, while on the other hand it has been shown that in any supersymmetric plasma there should exist a massless fermionic collective excitation, the phonino. Aim of this work is to unify these two approaches. For the Wess-Zumino model, it is shown that the phonino exists and contributes to the supersymmetric Ward-Takahashi identities in the right way displaying that supersymmetry is broken spontaneously with the phonino as the Goldstone fermion.
We use analytical bootstrap techniques to study supersymmetric monodromy defects in the critical Wess-Zumino model. In preparation for our main result we first study two related systems which are interesting on their own: general monodromy defects (no susy), and the $varepsilon$-expansion bootstrap for the Wess-Zumino model (no defects). For general monodromy defects we discuss some subtleties specific to the codimension two case. In particular, conformal blocks and the Lorentzian inversion formula have to be slightly modified in order to accommodate odd-spin operators that can have a non-zero one-point function. In the Wess-Zumino model we initiate the $varepsilon$-expansion bootstrap for four-point functions of chiral operators, with the goal of obtaining spectral information about the bulk theory. We then proceed to tackle the harder technical problem of analyzing monodromy defects in the presence of supersymmetry. We use inversion formula technology and spectral data coming from our four-point function analysis, in order to completely bootstrap two-point functions of chiral operators at leading order in $varepsilon$. Our result can be written in terms of novel special functions which we analyze in detail, and allows us to efficiently extract the CFT data that characterizes the correlator.
We consider a lattice formulation of the four dimensional N=1 Wess-Zumino model in terms of the Ginsparg-Wilson relation. This formulation has an exact supersymmetry on the lattice. The lattice action is invariant under a deformed supersymmetric transformation which is non-linear in the scalar fields and it is determined by an iterative procedure in the coupling constant to all orders in perturbation theory. We also show that the corresponding Ward-Takahashi identity is satisfied at fixed lattice spacing. The calculation is performed in lattice perturbation theory up to order $g^3$ (two-loop) and the Ward-Takahashi identity (containing 110 connected non-tadpole Feynman diagrams) is satisfied at fixed lattice spacing thanks to this exact lattice supersymmetry.
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