scholarly journals Shift-symmetric 𝖲𝖮(𝖭) multi-Galileon

2021 ◽  
Vol 2021 (12) ◽  
pp. 045
Author(s):  
Katsuki Aoki ◽  
Yusuke Manita ◽  
Shinji Mukohyama

Abstract A Poincarè invariant, local scalar field theory in which the Lagrangian and the equation of motion contain only up to second-order derivatives of the fields is called generalized Galileon. The covariant version of it in four dimensions is called Horndeski theory, and has been vigorously studied in applications to inflation and dark energy. In this paper, we study a class of multi-field extensions of the generalized Galileon theory. By imposing shift and SO(N) symmetries on all the currently known multi-Galileon terms in general dimensions, we find that the structure of the Lagrangian is uniquely determined and parameterized by a series of coupling constants. We also study tensor perturbation in the shift-symmetric SO(3) multi-Galileon theory in four dimensions. The tensor perturbations can obtain a mass term stemming from the same symmetry breaking pattern as the solid inflation. We also find that the shift-symmetric SO(3) multi-Galileon theory gives rise to new cubic interactions of the tensor modes, suggesting the existence of a new type of tensor primordial non-Gaussianity.

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Connor Behan ◽  
Pietro Ferrero ◽  
Xinan Zhou

Abstract Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1, 2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties. We point out that these maximally supersymmetric holographic correlators exhibit a hidden dimensional reduction structure à la Parisi and Sourlas. This emergent structure allows the correlators to be compactly expressed in terms of only scalar exchange diagrams in a dimensionally reduced spacetime, where formally both the AdS and the sphere factors have four dimensions less. We also demonstrate the superconformal properties of holographic correlators under the chiral algebra and topological twistings. For AdS5× S5 and AdS7× S4, we obtain closed form expressions for the meromorphic twisted correlators from the maximally R-symmetry violating limit of the holographic correlators. The results are compared with independent field theory computations in 4d $$ \mathcal{N} $$ N = 4 SYM and the 6d (2, 0) theory, finding perfect agreement. For AdS4× S7, we focus on an infinite family of near-extremal four-point correlators, and extract various protected OPE coefficients from supergravity. These OPE coefficients provide new holographic predictions to be matched by future supersymmetric localization calculations. In deriving these results, we also develop many technical tools which should have broader applicability beyond studying holographic correlators.


2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Marco Panero ◽  
Antonio Smecca

Abstract We present a high-precision Monte Carlo study of the classical Heisenberg model in four dimensions. We investigate the properties of monopole-like topological excitations that are enforced in the broken-symmetry phase by imposing suitable boundary conditions. We show that the corresponding magnetization and energy-density profiles are accurately predicted by previous analytical calculations derived in quantum field theory, while the scaling of the low-energy parameters of this description questions an interpretation in terms of particle excitations. We discuss the relevance of these findings and their possible experimental applications in condensed-matter physics.


2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Galvagno ◽  
Michelangelo Preti

Abstract We consider a family of $$ \mathcal{N} $$ N = 2 superconformal field theories in four dimensions, defined as ℤq orbifolds of $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the $$ \mathcal{N} $$ N = 1 superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of N , exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from $$ \mathcal{N} $$ N = 4 only at high orders in perturbation theory.


1974 ◽  
Vol 52 (24) ◽  
pp. 4062-4071 ◽  
Author(s):  
T. Bruce Grindley ◽  
Walter A. Szarek

The magnitude of —OCH2O— group geminal H,H coupling contants, the size of the vicinal coupling constants, and the tenets of conformational analysis were used to establish that in solution the conformation of the 1,3-dioxepane rings in derivatives of 1,3:2,5-di-O-methylenemannitol and 2,5-O-methylenemannitol is predominantly the twist-chair in which the C2 axis passes through the acetal carbon.


2001 ◽  
Vol 16 (11) ◽  
pp. 1951-1982 ◽  
Author(s):  
CHRISTOF WETTERICH

An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We present a simple unified description of critical phenomena for O(N)-symmetric scalar models in two, three or four dimensions, including essential scaling for the Kosterlitz-Thouless transition.


1976 ◽  
Vol 54 (14) ◽  
pp. 2228-2230 ◽  
Author(s):  
Ted Schaefer ◽  
J. Brian Rowbotham

The conformational preferences in CCl4 solution at 32 °C of the hydroxyl groups in bromine derivatives of 1,3-dihydroxybenzene are deduced from the long-range spin–spin coupling constants between hydroxyl protons and ring protons over five bonds. Two hydroxyl groups hydrogen bond to the same bromine substituent in 2-bromo-1,3-dihydroxybenzene but prefer to hydrogen bond to different bromine substituents when available, as in 2,4-dibromo-1,3-dihydroxybenzene. When the OH groups can each choose between two ortho bromine atoms, as in 2,4,6-tribromoresorcinol, they apparently do so in a very nearly statistical manner except that they avoid hydrogen bonding to the common bromine atom.


2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Zaid Laadjal ◽  
Qasem M. Al-Mdallal ◽  
Fahd Jarad

In this article, we use some fixed point theorems to discuss the existence and uniqueness of solutions to a coupled system of a nonlinear Langevin differential equation which involves Caputo fractional derivatives of different orders and is governed by new type of nonlocal and nonseparated boundary conditions consisting of fractional integrals and derivatives. The considered boundary conditions are totally dissimilar than the ones already handled in the literature. Additionally, we modify the Adams-type predictor-corrector method by implicitly implementing the Gauss–Seidel method in order to solve some specific particular cases of the system.


2018 ◽  
Vol 184 ◽  
pp. 01023
Author(s):  
Gordana V. Jelić ◽  
Vladica Stanojević ◽  
Dragana Radosavljević

One of the basic equations of mathematical physics (for instance function of two independent variables) is the differential equation with partial derivatives of the second order (3). This equation is called the wave equation, and is provided when considering the process of transverse oscillations of wire, longitudinal oscillations of rod, electrical oscillations in a conductor, torsional vibration at waves, etc… The paper shows how to form the equation (3) which is the equation of motion of each point of wire with abscissa x in time t during its oscillation. It is also shown how to determine the equation (3) in the task of electrical oscillations in a conductor. Then equation (3) is determined, and this solution satisfies the boundary and initial conditions.


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