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1. Alternate computation of gravitational effects from a single loop of inflationary scalars

   https://doi.org/10.1007/JHEP07(2024)099  

   Miao, S P; Tsamis, N C; Woodard, R P (July 2024, Journal of High Energy Physics)

   We present a new computation of the renormalized graviton self-energy induced by a loop of massless, minimally coupled scalars on de Sitter background. Our result takes account of the need to include a finite renormalization of the cosmological constant, which was not included in the first analysis. We also avoid preconceptions concerning structure functions and instead express the result as a linear combination of 21 tensor differential operators. By using our result to quantum-correct the linearized effective field equation we derive logarithmic corrections to both the electric components of the Weyl tensor for gravitational radiation and to the two potentials which quantify the gravitational response to a static point mass. 

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2. A PIE Representation of Scalar Quadratic PDEs and Global Stability Analysis Using SDP

   Jagt, Declan; Seiler, Peter; Peet, Matthew (December 2023, Proceedings of the IEEE Conference on Decision Control)

   It has recently been shown that the evolution of a linear Partial Differential Equation (PDE) can be more conveniently represented in terms of the evolution of a higher spatial derivative of the state. This higher spatial derivative (termed the `fundamental state') lies in $$L_2$$ - requiring no auxiliary boundary conditions or continuity constraints. Such a representation (termed a Partial Integral Equation or PIE) is then defined in terms of an algebra of bounded integral operators (termed Partial Integral (PI) operators) and is constructed by identifying a unitary map from the fundamental state to the state of the original PDE. Unfortunately, when the PDE is nonlinear, the dynamics of the associated fundamental state are no longer parameterized in terms of PI operators. However, in this paper we show that such dynamics can be compactly represented using a new tensor algebra of partial integral operators acting on the tensor product of the fundamental state. We further show that this tensor product of the fundamental state forms a natural distributed equivalent of the monomial basis used in representation of polynomials on a finite-dimensional space. This new representation is then used to provide a simple SDP-based Lyapunov test of stability of quadratic PDEs. The test is applied to three illustrative examples of quadratic PDEs. 

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3. Linearized boundary control method for density reconstruction in acoustic wave equations

   https://doi.org/10.1088/1361-6420/ad98bc  

   Oksanen, Lauri; Yang, Tianyu; Yang, Yang (December 2024, Inverse Problems)

   Abstract We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the linearized Neumann-to-Dirichlet map. A key ingredient in the derivation is a linearized Blagoves̆c̆enskiĭ’s identity with a free parameter. When the linearization is at a constant background density, we derive two reconstructive algorithms with stability estimates based on the boundary control method. When the linearization is at a non-constant background density, we establish an increasing stability estimate for the recovery of the density perturbation. The proposed reconstruction algorithms are implemented and validated with several numerical experiments to demonstrate the feasibility. 

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4. Holographic thermal correlators revisited

   https://doi.org/10.1007/JHEP11(2021)139  

   Krishna, Hare; Rodriguez-Gomez, D. (November 2021, Journal of High Energy Physics)

   A bstract We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator O k and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of T n O k (being T n the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way. 

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5. Hidden U(N) symmetry behind $$ \mathcal{N} $$ = 1 superamplitudes

   https://doi.org/10.1007/JHEP11(2023)215  

   Delgado, Antonio; Martin, Adam; Wang, Runqing (November 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> In this paper we develop a Young diagram approach to constructing higher dimensional operators formed from massless superfields and their superderivatives in$$ \mathcal{N} $$ $N$= 1 supersymmetry. These operators are in one-to-one correspondence with non-factorizable terms in on-shell superamplitudes, which can be studied with massless spinor helicity techniques. By relating all spin-helicity variables to certain representations under a hidden U(N) symmetry behind the theory, we show each non-factorizable superamplitude can be identified with a specific Young tableau. The desired tableau is picked out of a more general set of U(N) tensor products by enforcing the supersymmetric Ward identities. We then relate these Young tableaux to higher dimensional superfield operators and list the rules to read operators directly from Young tableau. Using this method, we present several illustrative examples. 

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