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Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 501
Author(s):  
Stanislav Alexeyev ◽  
Daniil Krichevskiy ◽  
Boris Latosh

Validity of three gravity models with non-linear realization of conformal symmetry previously discussed in literature is addressed. Two models are found to be equivalent up to a change of coset coordinates. It was found that models contain ghost degrees of freedom that may be excluded by an introduction of an additional symmetry to the target space. One model found to be safe in early universe. The others found to lack spin-2 degrees of freedom and to have peculiar coupling to matter degrees of freedom.


Author(s):  
Hui Xing ◽  
Alireza Azizi ◽  
Roya Momen ◽  
Tianlv Xu ◽  
Steven Kirk ◽  
...  

We investigate the presence of helical character and chirality using a vector-based charge density perspective instead of energetic or structural measures. The vector-based perspective of the chemical bonding, constructed using the most preferred direction of charge density accumulation, finds the presence of induced symmetry-breaking for α,ω-disubstituted [4]cumulenes as the end groups are torsioned. The stress tensor trajectories Tσ(s) are used to provide the additional symmetry-breaking required to quantify the degree and nature of the chirality and helical character. We find an absence of chirality for [4]cumulene but a very significant degree of axiality as demonstrated by the purely axial form of the Tσ(s) indicating a lack of helical character. The S-1,5-dimethyl-[4]cumulene contains a very low degree of chiral character but significant axiality(helicity) resulting in a weakly helical morphology of the corresponding Tσ(s). The (-)S(-), (+)S(-) and (+)S(+) conformations of S-1,5-diamino-[4]cumulene contain very significant degrees of both chirality and helical character resulting in helical morphology of the corresponding Tσ(s). The chirality assignments are in agreement with the Cahn–Ingold–Prelog (CIP) classifications for the (-)S(-), (+)S(-) and (+)S(+) conformations of S-1,5-diamino-[4]cumulene. We discuss the consequences for the Tσ(s) in locating chiral character in these molecules in future experiment investigations.


2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Saniya Batra ◽  
Prakriti Rai

Several mathematicians have extensively investigated polynomials, their extensions, and their applications in various other research areas for a decade. Our paper aims to introduce another such polynomial, namely, Laguerre-based generalized Humbert polynomial, and investigate its properties. In particular, it derives elementary identities, recursive differential relations, additional symmetry identities, and implicit summation formulas.


Author(s):  
Meiyan Hu ◽  
Chuanzhong Li

This paper aims at additional symmetries of the unextended and extended, commutative and noncommutative dispersionless Gelfand–Dickey (dGD) hierarchies. Being similar to the Lax formalism of the Gelfand–Dickey (GD) hierarchy, we construct the function [Formula: see text] and Orlov–Schulman function [Formula: see text] of the hierarchies. Meanwhile, the additional symmetry will be studied with the infinite flows of [Formula: see text] and [Formula: see text] function of the dGD hierarchy and one can find that only a part of additional flows can survive under the GD constraints with the corresponding string equation. Furthermore, we pay attention to the additional symmetries of the dispersionless extended Gelfand–Dickey (dEGD) hierarchy which has a quantum torus algebraic structure and show the flows in detail. The additional symmetry of dispersionless noncommutative Gelfand–Dickey (dNCGD) hierarchy and dispersionless extended noncommutative Gelfand–Dickey (dENCGD) hierarchy are studied.


Author(s):  
E. Basso ◽  
Daniel J. H. Chung

Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of U(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an [Formula: see text] permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame-dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.


Author(s):  
Meiyan Hu ◽  
Chuanzhong Li

In this paper, we construct the Lax operator of the multi-component Boussinesq hierarchy. Based on the Sato theory and the dressing structure of the multi-component Boussinesq hierarchy, the adjoint wave function and the Orlov–Schulman’s operator are introduced, which are useful for constructing the additional symmetry of the multi-component Boussinesq hierarchy. Besides, the additional flows can commute with the original flows, and these flows form an infinite dimensional [Formula: see text] algebra. Taking the above discussion into account, we mainly study the additional symmetry flows and the generating function for both strongly and weakly multi-component of the Boussinesq hierarchies. By the way, using the [Formula: see text] constraint of the multi-component Boussinesq hierarchy, the string equation can be derived.


2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Po-Shen Hsin ◽  
Ho Tat Lam

Gauge theories in various dimensions often admit discrete theta angles, that arise from gauging a global symmetry with an additional symmetry protected topological (SPT) phase. We discuss how the global symmetry and ’t Hooft anomaly depends on the discrete theta angles by coupling the gauge theory to a topological quantum field theory (TQFT). We observe that gauging an Abelian subgroup symmetry, that participates in symmetry extension, with an additional SPT phase leads to a new theory with an emergent Abelian symmetry that also participates in a symmetry extension. The symmetry extension of the gauge theory is controlled by the discrete theta angle which comes from the SPT phase. We find that discrete theta angles can lead to two-group symmetry in 4d4d QCD with SU(N),SU(N)/\mathbb{Z}_kSU(N),SU(N)/ℤk or SO(N)SO(N) gauge groups as well as various 3d3d and 2d2d gauge theories.


2020 ◽  
Vol 229 (21) ◽  
pp. 3187-3203
Author(s):  
Katri Huitu

AbstractThe left-right symmetric models extend the gauge group of the Standard Model enabling treatment of the left- and right-handed fermions in the same footing. The left-right symmetry requires the existence of right-handed neutrinos, leading naturally to non-zero masses for neutrinos. Here some aspects of a supersymmetric version of the left-right symmetric models are reviewed. Such models have many virtues, including possibility for dark matter without any new additional symmetry needed in order to have a stable lightest supersymmetric particle. In the model the lightest sneutrino or the lightest neutralino can form dark matter of the universe, at the same time fulfilling all the experimental constraints. The dark matter particle in the model can be very different from the dark matter typical in the minimal supersymmetric standard model. Specific signals for this kind of models at the LHC are also discussed.


2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Tanguy Grall ◽  
Sadra Jazayeri ◽  
David Stefanyszyn

Abstract In contrast to massless spinning particles, scalars are not heavily constrained by unitarity and locality. Off-shell, no gauge symmetries are required to write down manifestly local theories, while on-shell consistent factorisation is trivial. Instead a useful classification scheme for scalars is based on the symmetries they can non-linearly realise. Motivated by the breaking of Lorentz boosts in cosmology, in this paper we classify the possible symmetries of a shift-symmetric scalar that is assumed to non-linearly realise Lorentz boosts as, for example, in the EFT of inflation. Our classification method is algebraic; guided by the coset construction and inverse Higgs constraints. We rediscover some known phonon theories within the superfluid and galileid classes, and discover a new galileid theory which we call the extended galileid. Generic galileids correspond to the broken phase of galileon scalar EFTs and our extended galileids correspond to special subsets where each galileon coupling is fixed by an additional symmetry. We discuss the broken phase of theories that also admit a perturbation theory around Poincaré invariant vacua and we show that the so-called exceptional EFTs, the DBI scalar and special galileon, do not admit such a broken phase. Concentrating on DBI we provide a detailed account of this showing that the scattering amplitudes are secretly Poincaré invariant when the theory is expanded around the superfluid background used in the EFT of inflation. We point out that DBI is an exception to the common lore that the residue of the total energy pole of cosmological correlators is proportional to the amplitude. We also discuss the inevitability of poles in 2 → 2 scattering amplitudes when boost are spontaneously broken meaning that such theories do not admit Adler zeros and generalisations even in the presence of a shift symmetry.


2020 ◽  
Vol 10 (3) ◽  
Author(s):  
Cong Li ◽  
Xianxin Wu ◽  
Le Wang ◽  
Defa Liu ◽  
Yongqing Cai ◽  
...  

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