arXiv subjects

Alexey Sharapov

Publications and source records attributed to Alexey Sharapov.

21 records · Page 2Linked to original sources

arXiv2020

Towards Massless Sector of Tensionless Strings on $AdS_5$

{A} Higher Spin Gravity in five dimensions is constructed. It was shown recently that constructing formally consistent classical equations of motion of higher spin gravities is equivalent to finding a certain deformation of a given higher spin algebra. A strong homotopy algebra encoding the interaction vertices then follows. We propose two different and novel realizations of the deformed higher spin algebra in the case of five dimensions: one in terms of the universal enveloping algebra of $su(2,2)$ and the other by means of oscillator variables. Both the new realizations admit supersymmetric extensions and the $\mathcal{N}=8$ case underlies the massless sector of tensionless strings.

hep-th↗

arXiv2019

$A_\infty$ Algebras from Slightly Broken Higher Spin Symmetries

We define a class of $A_\infty$-algebras that are obtained by deformations of higher spin symmetries. While higher spin symmetries of a free CFT form an associative algebra, the slightly broken higher spin symmetries give rise to a minimal $A_\infty$-algebra extending the associative one. These $A_\infty$-algebras are related to non-commutative deformation quantization much as the unbroken higher spin symmetries result from the conventional deformation quantization. In the case of three dimensions there is an additional parameter that the $A_\infty$-structure depends on, which is to be related to the Chern-Simons level. The deformations corresponding to the bosonic and fermionic matter lead to the same $A_\infty$-algebra, thus manifesting the three-dimensional bosonization conjecture. In all other cases we consider, the $A_\infty$-deformation is determined by a generalized free field in one dimension lower.

hep-th↗

arXiv2014

Peierls brackets in non-Lagrangian field theory

The concept of Lagrange structure allows one to systematically quantize the Lagrangian and non-Lagrangian dynamics within the path-integral approach. In this paper, I show that any Lagrange structure gives rise to a covariant Poisson brackets on the space of solutions to the classical equations of motion, be they Lagrangian or not. The brackets generalize the well-known Peierls' bracket construction and make a bridge between the path-integral and the deformation quantization of non-Lagrangian dynamics.

hep-th↗