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Concept# Unitarity gauge

Summary

In theoretical physics, the unitarity gauge or unitary gauge is a particular choice of a gauge fixing in a gauge theory with a spontaneous symmetry breaking. In this gauge, the scalar fields responsible for the Higgs mechanism are transformed into a basis in which their Goldstone boson components are set to zero. In other words, the unitarity gauge makes the manifest number of scalar degrees of freedom minimal.
The gauge was introduced to particle physics by Steven Weinberg in the context of the electroweak theory. In electroweak theory, the degrees of freedom in a unitarity gauge are the massive spin-1 W+, W− and Z bosons with three polarizations each, the photon with two polarizations, and the scalar Higgs boson.
The unitarity gauge is usually used in tree-level calculations. For loop calculations, other gauge choices such as the 't Hooft–Feynman gauge often reduce the mathematical complexity of the calculation.

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PHYS-416: Particle physics II

Presentation of the electroweak and strong interaction theories that constitute the Standard Model of particle physics. The course also discusses the new theories proposed to solve the problems of the Standard Model.

PHYS-432: Quantum field theory II

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions.

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We explore the space of consistent three-particle couplings in Z(2)-symmetric two-dimensional QFTs using two first-principles approaches. Our first approach relies solely on unitarity, analyticity and crossing symmetry of the two-to-two scattering amplitudes and extends the techniques of [2] to a multi-amplitude setup. Our second approach is based on placing QFTs in AdS to get upper bounds on couplings with the numerical conformal bootstrap, and is a multi-correlator version of [1]. The space of allowed couplings that we carve out is rich in features, some of which we can link to amplitudes in integrable theories with a Z(2) symmetry, e.g., the three-state Potts and tricritical Ising field theories. Along a specific line our maximal coupling agrees with that of a new exact S-matrix that corresponds to an elliptic deformation of the supersymmetric Sine-Gordon model which preserves unitarity and solves the Yang-Baxter equation.

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We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of the matrix of inner products between asymptotic states (in and out) and states created by the action of local operators on the vacuum. The corresponding matrix elements involve scattering amplitudes, form factors and spectral densities of local operators. We test this method in two-dimensional QFTs by setting up a linear optimization problem that gives a lower bound on the central charge of the UV CFT associated to a QFT with a given mass spectrum of stable particles (and couplings between them). Some of our numerical bounds are saturated by known form factors in integrable theories like the sine-Gordon, E-8 and O(N) models.

We use the S-matrix bootstrap to carve out the space of unitary, crossing symmetric and supersymmetric graviton scattering amplitudes in ten dimensions. We focus on the leading Wilson coefficient a controlling the leading correction to maximal supergravity. The negative region alpha < 0 is excluded by a simple dual argument based on linearized unitarity (the desert). Awhole semi-infinite region alpha greater than or similar to 0.14 is allowed by the primal bootstrap (the garden). A finite intermediate region is excluded by nonperturbative unitarity (the swamp). Remarkably, string theory seems to cover all (or at least almost all) the garden from very large positive a-at weak coupling-to the swamp boundary-at strong coupling.