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Abstract For a given material,controllable deformationsare those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials,universal deformationsare those deformations that are controllable for any material within the class. In this paper, we characterize the universal deformations in compressible isotropic implicit elasticity defined by solids whose constitutive equations, in terms of the Cauchy stress$$\varvec{\sigma }$$ and the left Cauchy-Green strain$$\textbf{b}$$ , have the implicit form$$\varvec{\textsf{f}}(\varvec{\sigma },\textbf{b})=\textbf{0}$$ . We prove that universal deformations are homogeneous. However, an important observation is that, unlike Cauchy (and Green) elasticity, not every homogeneous deformation is constitutively admissible for a given implicit-elastic solid. In other words, the set of universal deformations is material-dependent, yet it remains a subset of homogeneous deformations.
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This content will become publicly available on August 1, 2026
Higher-spin currents and flows in auxiliary field sigma models
A<sc>bstract</sc> We study local, higher-spin conserved currents in integrable 2dsigma models that have been deformed via coupling to auxiliary fields. These currents generate integrability-preserving flows introduced by Smirnov and Zamolodchikov. For auxiliary field (AF) deformations of a free boson, we prove that local spin-ncurrents exist for allnand give recursion relations that characterize Smirnov-Zamolodchikov (SZ) flows driven by these currents. We then show how to construct spin-2ncurrents in a unified class of auxiliary field sigma models with common structure — including AF theories based on the principal chiral model (PCM), its non-Abelian T-dual, (bi-)Yang-Baxter deformations of the PCM, and symmetric space models — for interaction functions of one variable, and describe SZ flows driven by any function of the stress tensor in these cases. Finally, we give perturbative solutions for spin-3 SZ flows in any member of our unified class of AF models with underlying$$ \mathfrak{su} $$ (3) algebra. Part of our analysis shows that the class of AF deformations can be extended by allowing the interaction function to depend on a larger set of variables than has previously been considered.
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- Award ID(s):
- 2019786
- PAR ID:
- 10648143
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2025
- Issue:
- 8
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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