Explore the vast range of titles available.

The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over

Non-Abelian gauge theories, such as quantum chromodynamics (QCD) or electroweak theory, are best studied with the aid of Green's functions that are gauge-invariant off-shell, but unlike for the photon in quantum electrodynamics, conventional graphical constructions fail. The Pinch Technique provides a systematic framework for constructing such Green's functions, and has many useful applications. Beginning with elementary one-loop examples, this book goes on to extend the method to all orders, showing that the Pinch Technique is equivalent to calculations in the background field Feynman gauge. The Pinch Technique Schwinger-Dyson equations are derived, and used to show how a dynamical gluon mass arises in QCD. Applications are given to the center vortex picture of confinement, the gauge-invariant treatment of resonant amplitudes, the definition of non-Abelian effective charges, high-temperature effects, and even supersymmetry. This book is ideal for elementary particle theorists and graduate students.

Soft machines are a promising design paradigm for human-centric devices 1 , 2 and systems required to interact gently with their environment 3 , 4 . To enable soft machines to respond intelligently to their surroundings, compliant sensory feedback mechanisms are needed. Specifically, soft alternatives to strain gauges—with high resolution at low strain (less than 5 per cent)—could unlock promising new capabilities in soft systems. However, currently available sensing mechanisms typically possess either high strain sensitivity or high mechanical resilience, but not both. The scarcity of resilient and compliant ultra-sensitive sensing mechanisms has confined their operation to laboratory settings, inhibiting their widespread deployment. Here we present a versatile and compliant transduction mechanism for high-sensitivity strain detection with high mechanical resilience, based on strain-mediated contact in anisotropically resistive structures (SCARS). The mechanism relies upon changes in Ohmic contact between stiff, micro-structured, anisotropically conductive meanders encapsulated by stretchable films. The mechanism achieves high sensitivity, with gauge factors greater than 85,000, while being adaptable for use with high-strength conductors, thus producing sensors resilient to adverse loading conditions. The sensing mechanism also exhibits high linearity, as well as insensitivity to bending and twisting deformations—features that are important for soft device applications. To demonstrate the potential impact of our technology, we construct a sensor-integrated, lightweight, textile-based arm sleeve that can recognize gestures without encumbering the hand. We demonstrate predictive tracking and classification of discrete gestures and continuous hand motions via detection of small muscle movements in the arm. The sleeve demonstration shows the potential of the SCARS technology for the development of unobtrusive, wearable biomechanical feedback systems and human–computer interfaces. Strain gauges with both high sensitivity and high mechanical resilience, based on strain-mediated contact in anisotropically resistive structures, are demonstrated within a sensor-integrated, textile-based sleeve that can recognize human hand motions via muscle deformations.

Palabras clave: catolicismo, Dominicos, Guatemala, historia sensorial, México, paisajes sonoros, protestantismo, Thomas Gage.

A bstract We use the 5-sphere partition functions of supersymmetric Yang-Mills theories to explore the (2, 0) superconformal theory on S 5 × S 1 . The 5d theories can be regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a special limit, the perturbative partition function takes the form of the Chern-Simons partition function on S 3 . With a simple non-perturbative completion, it becomes a 6d index which captures the degeneracy of a sector of BPS states as well as the index version of the vacuum Casimir energy. The Casimir energy exhibits the N 3 scaling at large N . The large N index for U( N ) gauge group also completely agrees with the supergravity index on AdS 7 × S 4 .

The Kitaev quantum spin liquid (KQSL) is an exotic emergent state of matter exhibiting Majorana fermion and gauge flux excitations. The magnetic insulator α-RuCl3 is thought to realize a proximate KQSL. We used neutron scattering on single crystals of α-RuCl3 to reconstruct dynamical correlations in energy-momentum space. We discovered highly unusual signals, including a column of scattering over a large energy interval around the Brillouin zone center, which is very stable with temperature. This finding is consistent with scattering from the Majorana excitations of a KQSL. Other, more delicate experimental features can be transparently associated with perturbations to an ideal model. Our results encourage further study of this prototypical material and may open a window into investigating emergent magnetic Majorana fermions in correlated materials.The Kitaev quantum spin liquid (KQSL) is an exotic emergent state of matter exhibiting Majorana fermion and gauge flux excitations. The magnetic insulator α-RuCl3 is thought to realize a proximate KQSL. We used neutron scattering on single crystals of α-RuCl3 to reconstruct dynamical correlations in energy-momentum space. We discovered highly unusual signals, including a column of scattering over a large energy interval around the Brillouin zone center, which is very stable with temperature. This finding is consistent with scattering from the Majorana excitations of a KQSL. Other, more delicate experimental features can be transparently associated with perturbations to an ideal model. Our results encourage further study of this prototypical material and may open a window into investigating emergent magnetic Majorana fermions in correlated materials.

A bstract We extend recent work on the relation of 4 d and 3 d IR dualities of supersymmetric gauge theories with four supercharges to the case of orthogonal gauge groups. The distinction between different SO( N ) gauge theories in 4 d plays an important role in this relation. We show that the 4 d duality leads to a 3 d duality between an SO( N c ) gauge theory with N f flavors and an SO( N f − N c + 2) theory with N f flavors and extra singlets, and we derive its generalization in the presence of Chern-Simons terms. There are two different O ( N ) theories in 3 d , which we denote by O ( N ) ± , and we also show that the O ( N c ) − gauge theory is dual to a Spin( N f − N c + 2) theory, and derive from 4 d the known duality between O ( N c ) + and O ( N f − N c + 2) + . We verify the consistency of these 3 d dualities by various methods, including index computations.

Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a generalized, subsystem version of color codes. In 3D they allow the transversal implementation of a universal set of gates by gauge fixing, while error-dectecting measurements involve only four or six qubits.

Protection of gauge invariance in experimental realizations of lattice gauge theories based on energy-penalty schemes has recently stimulated impressive efforts both theoretically and in setups of quantum synthetic matter. A major challenge is the reliability of such schemes in non-abelian gauge theories where local conservation laws do not commute. Here, we show through exact diagonalization (ED) that non-abelian gauge invariance can be reliably controlled using gauge-protection terms that energetically stabilize the target gauge sector in Hilbert space, suppressing gauge violations due to unitary gauge-breaking errors. We present analytic arguments that predict a volume-independent protection strength V , which when sufficiently large leads to the emergence of an adjusted gauge theory with the same local gauge symmetry up to least a timescale ∝ V / V 0 3 . Thereafter, a renormalized gauge theory dominates up to a timescale ∝exp( V / V 0 )/ V 0 with V 0 a volume-independent energy factor, similar to the case of faulty abelian gauge theories. Moreover, we show for certain experimentally relevant errors that single-body protection terms robustly suppress gauge violations up to all accessible evolution times in ED, and demonstrate that the adjusted gauge theory emerges in this case as well. These single-body protection terms can be readily implemented with fewer engineering requirements than the ideal gauge theory itself in current ultracold-atom setups and noisy intermediate-scale quantum (NISQ) devices.

A bstract We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the Z N gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the Z N gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.