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- Fardelli, Giulia, 1994-
(author)
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A CFT perspective on holographic correlators
- 2023
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Doctoral thesis (other academic/artistic)abstract
- Conformal symmetry is ubiquitous in physics. It emerges in a variety of situations from critical phenomena, through condensed matter systems and jets at the LHC to string theory. Conformal field theories (CFTs) describe the universal behavior underlying these very different setups. An efficient and powerful way to study CFTs is represented by the conformal bootstrap. This non-perturbative technique allows constraining a CFT just relying on its own symmetries and a set of consistency conditions such as unitarity, crossing symmetry and the operator product expansion.In this thesis, we discuss applications of analytic bootstrap techniques to holographic superconformal field theories, which possess an additional space-time symmetry, known as supersymmetry, besides the conformal one. Through the AdS/CFT correspondence, these theories are dual to quantum gravity in AdS such that the analysis of CFT correlators gives access to gravitational amplitudes in curved space-time. We will see how the existence of a protected sector in such theories greatly simplifies the problem and allows us to bootstrap these observables.In this work, we devote our attention to the study of four-point functions in N=4 super Yang Mills (SYM) and in N=2 theories in four dimensions. In the first part of the thesis, we review the basics of superconformal algebra and superspace and then we introduce the main analytic bootstrap tool, the Lorentzian inversion formula. In the second part, after a brief description of the spectrum of N=4 SYM and its holographic realization in AdS, we focus on the correlator of four gravitons. We thoroughly analyze this four-point function in the supergravity approximation and as an expansion at large central charge. We conclude with a discussion of less supersymmetric correlators involving so-called quarter-BPS operators. In the last part instead, we change the setting and we study correlators of spinning operators belonging to the flavor current multiplet in N=2 superconformal theories. By using analytic superspace techniques, we build the four-point function of gluon superfields and, from that, we extract correlators of all component fields, including the four-current one. In the end, we comment on the existence of an AdS double copy connecting these gluon amplitudes with their gravitational counterpart in N=4 SYM.
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| 2. |
- Larsen, Kasper J.
(author)
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Maximal Unitarity at Two Loops : A New Method for Computing Two-Loop Scattering Amplitudes
- 2012
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Doctoral thesis (other academic/artistic)abstract
- The study of scattering amplitudes beyond one loop is necessary for precision phenomenology for the Large Hadron Collider and may also provide deeper insights into the theoretical foundations of quantum field theory. In this thesis we develop a new method for computing two-loop amplitudes, based on unitarity rather than Feynman diagrams. In this approach, the two-loop amplitude is first expanded in a linearly independent basis of integrals. The process dependence thereby resides in the coefficients of the integrals. These expansion coefficients are then the object of calculation.Our main results include explicit formulas for a subset of the integral coefficients, expressing them as products of tree-level amplitudes integrated over specific contours in the complex plane. We give a general selection principle for determining these contours. This principle is then applied to obtain the coefficients of integrals with the topology of a double box. We show that, for four-particle scattering, each double-box integral in the two-loop basis is associated with a uniquely defined complex contour, referred to as its master contour. We provide a classification of the solutions to setting all propagators of the general double-box integral on-shell. Depending on the number of external momenta at the vertices of the graph, these solutions are given as a chain of pointwise intersecting Riemann spheres, or a torus. This classification is needed to define master contours for amplitudes with arbitrary multiplicities.We point out that a basis of two-loop integrals with as many infrared finite elements as possible allows substantial technical simplications, in terms of obtaining the coefficients of the integrals, as well as for the analytic evaluation of the integrals themselves. We compute two such integrals at four points, obtaining remarkably compact expressions. Finally, we provide a check on a recently developed recursion relation for the all-loop integrand of the amplitudes of N=4 supersymmetric Yang-Mills theory, examining the two-loop six-gluon MHV amplitude and finding agreement. The validity of the approach to two-loop amplitudes developed in this thesis extends to all four-dimensional gauge theories, in particular QCD. The approach is suited for obtaining compact analytical expressions as well as for numerical implementations.
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| 3. |
- Travaglini, Gabriele, et al.
(author)
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The SAGEX review on scattering amplitudes
- 2022
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In: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 55:44
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Research review (peer-reviewed)abstract
- This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of current (2022) research and developments.
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