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Author

Otto Nachtmann

Other affiliations: Institute for Advanced Study
Bio: Otto Nachtmann is an academic researcher from Cornell University. The author has contributed to research in topics: Operator product expansion & Moment problem. The author has an hindex of 1, co-authored 1 publications receiving 383 citations. Previous affiliations of Otto Nachtmann include Institute for Advanced Study.

Papers
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Journal ArticleDOI
TL;DR: Wilson's operator product expansion is examined in this article, where it is shown how to project on operators of definite spin at finite Q2 consistency conditions for anomalous dimensions following from positivity using the moment problem.

409 citations


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Book
30 May 2011
TL;DR: In this article, a systematic treatment of perturbative QCD is given, giving an accurate account of the concepts, theorems and their justification, giving strong motivations for the methods.
Abstract: The most non-trivial of the established microscopic theories of physics is QCD: the theory of the strong interaction. A critical link between theory and experiment is provided by the methods of perturbative QCD, notably the well-known factorization theorems. Giving an accurate account of the concepts, theorems and their justification, this book is a systematic treatment of perturbative QCD. As well as giving a mathematical treatment, the book relates the concepts to experimental data, giving strong motivations for the methods. It also examines in detail transverse-momentum-dependent parton densities, an increasingly important subject not normally treated in other books. Ideal for graduate students starting their work in high-energy physics, it will also interest experienced researchers wanting a clear account of the subject.

928 citations

Journal ArticleDOI
TL;DR: In this article, the constraints of crossing symmetry and unitarity in general 3D conformal field theories were studied, and it was shown that the 3D Ising model lies at a corner point on the boundary of the allowed parameter space.
Abstract: We study the constraints of crossing symmetry and unitarity in general 3D conformal field theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for their computation in arbitrary space-time dimension. Comparing the resulting bounds on operator dimensions and product-expansion coefficients in 3D to known results, we find that the 3D Ising model lies at a corner point on the boundary of the allowed parameter space. We also derive general upper bounds on the dimensions of higher spin operators, relevant in the context of theories with weakly broken higher spin symmetries.

862 citations

Journal ArticleDOI
TL;DR: The generalized parton distribution (GPD) as discussed by the authors was introduced as a universal tool to describe hadrons in terms of quark and gluonic degrees of freedom, and has been used for a long time in studies of hadronic structure.

705 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that every CFT with a scalar operator ϕ must contain infinite sequences of operators with twist approaching τ → 2Δ + 2n for each integer n as l → ∞.
Abstract: We take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| ≪ |υ| < 1. We prove that every CFT with a scalar operator ϕ must contain infinite sequences of operators $ {{\mathcal{O}}_{{\tau, \ell }}} $ with twist approaching τ → 2Δ ϕ + 2n for each integer n as l → ∞. We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the ϕ × ϕ OPE, and we discuss SCFTs and the 3d Ising Model as examples. Additionally, we show that the OPE coefficients of other large spin operators appearing in the OPE are bounded as l → ∞. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.

646 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the dimensions of unitary higher-dimensional conformal field theories (CFTs) via the crossing equations in the light-cone limit and found that CFTs become free at large spin and 1/s is a weak coupling parameter.
Abstract: We consider several aspects of unitary higher-dimensional conformal field theories (CFTs). We first study massive deformations that trigger a flow to a gapped phase. Deep inelastic scattering in the gapped phase leads to a convexity property of dimensions of spinning operators of the original CFT. We further investigate the dimensions of spinning operators via the crossing equations in the light-cone limit. We find that, in a sense, CFTs become free at large spin and 1/s is a weak coupling parameter. The spectrum of CFTs enjoys additivity: if two twists τ 1, τ 2 appear in the spectrum, there are operators whose twists are arbitrarily close to τ 1 + τ 2. We characterize how τ 1 + τ 2 is approached at large spin by solving the crossing equations analytically. We find the precise form of the leading correction, including the prefactor. We compare with examples where these observables were computed in perturbation theory, or via gauge-gravity duality, and find complete agreement. The crossing equations show that certain operators have a convex spectrum in twist space. We also observe a connection between convexity and the ratio of dimension to charge. Applications include the 3d Ising model, theories with a gravity dual, SCFTs, and patterns of higher spin symmetry breaking.

607 citations