This graduate textbook presents a comprehensive, unified treatment of the materials science of deformation as applied to solid Earth geophysics and geology. The deformation of Earth materials is ...presented in a systematic way covering elastic, anelastic and viscous deformation. Advanced discussions on relevant debates are also included to bring readers a full picture of science in this interdisciplinary area. This textbook is ideal for graduate courses on the rheology and dynamics of solid Earth, and includes review questions with solutions so readers can monitor their understanding of the material presented. It is also a much-needed reference for geoscientists in many fields including geology, geophysics, geochemistry, materials science, mineralogy and ceramics.
The relationship between T¯T deformations and the uniform light-cone gauge, first noted by Baggio and Sfondrini Phys. Rev. D 98, 021902 (2018), provides a powerful generating technique for deformed ...models. We recall this construction, distinguishing between changes of the gauge frame, which do not affect the theory, and genuine deformations. We investigate the geometric interpretation of the latter and argue that they affect the global features of the geometry before gauge fixing. Exploiting a formal relation between uniform light-cone gauge and static gauge in a T-dual frame, we interpret such a change as a T-duality–shift– T-duality transformation involving the two light-cone coordinates. In the static-gauge picture, the T¯T Castillejo-Dalitz-Dyson factor then has a natural interpretation as a Drinfeld-Reshetikhin twist of the worldsheet S matrix. To illustrate these ideas, we find the geometries yielding a T¯T deformation of the worldsheet S matrix of pp-wave and Lin-Lunin-Maldacena backgrounds.
We review recent attempts at dealing with the sign problem in Monte Carlo calculations by deforming the region of integration in the path integral from real to complex fields. We discuss the ...theoretical foundations, the algorithmic issues and present some results for low dimensional field theories in both imaginary and real time.
We consider current-current deformations that generalize T ¯ T ones, and show that they may be also introduced for integrable spin chains. In analogy with the integrable QFT setup, we define the ...deformation as a modification of the S matrix in the Bethe equations. Using results by Bargheer, Beisert and Loebbert we show that the deforming operator is composite and constructed out of two currents on the lattice; its expectation value factorizes like for T ¯ T . Such a deformation may be considered for any combination of charges that preserve the model's integrable structure.
One strategy for reducing the sign problem in finite-density field theories is to deform the path integral contour from real to complex fields. If the deformed manifold is the appropriate combination ...of Lefschetz thimbles-or somewhat close to them-the sign problem is alleviated. Gauge theories require generalizing the definition of thimble decompositions, and therefore it is unclear how to carry out a generalized thimble method. In this paper we discuss some of the conceptual issues involved by applying this method to QED1+1 at finite density, showing that the generalized thimble method yields correct results with less computational effort than standard methods.
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