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We associate vertex operators to space-time diffeomorphisms in flat space string theory, and compute their algebra, which is a diffeomorphism algebra with higher derivative corrections. As an application, we realize the asymptotic symmetry group BMS3 of three-dimensional flat space in terms of vertex operators on the string worldsheet. This provides an embedding of the BMS3 algebra in a consistent theory of quantum gravity. Higher derivative corrections vanish asymptotically. An appendix is dedicated to alpha prime corrected algebras in conformal field theory and string theory.
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In this note we address the question whether one can recover from the vertex operator algebra associated with a four-dimensional N=2 superconformal field theory the deformation quantization of the Higgs branch of vacua that appears as a protected subsector in the three-dimensional circle-reduced theory. We answer this question positively if the UV R-symmetries do not mix with accidental (topological) symmetries along the renormalization group flow from the four-dimensional theory on a circle to the three-dimensional theory. If they do mix, we still find a deformation quantization but at different values of its period.
Using the expressions for generalized ADT current and potential in a self consistent manner, we derive the asymptotic symmetry algebra on AdS$_3$ and the near horizon extremal BTZ spacetimes. The structure of symmetry algebra among the conserved charges for asymptotic killing vectors matches exactly with the known results thus establishing the algebraic equivalence between the well known existing formalisms for obtaining the conserved charges and the generalized ADT charges.
Let $G$ be a compact connected Lie group. The question of when a weighted Fourier algebra on $G$ is completely isomorphic to an operator algebra will be investigated in this paper. We will demonstrate that the dimension of the group plays an important role in the question. More precisely, we will get a positive answer to the question when we consider a polynomial type weight coming from a length function on $G$ with the order of growth strictly bigger than the half of the dimension of the group. The case of SU(n) will be examined, focusing more on the details including negative results. The proof for the positive directions depends on a non-commutative version of Littlewood multiplier theory, which we will develop in this paper, and the negative directions will be taken care of by restricting to a maximal torus.
We make a careful study of one-parameter isometry groups on Banach spaces, and their associated analytic generators, as first studied by Cioranescu and Zsido. We pay particular attention to various, subtly different, constructions which have appeared in the literature, and check that all give the same notion of generator. We give an exposition of the smearing technique, checking that ideas of Masuda, Nakagami and Woronowicz hold also in the weak$^*$-setting. We are primarily interested in the case of one-parameter automorphism groups of operator algebras, and we present many applications of the machinery, making the argument that taking a structured, abstract approach can pay dividends. A motivating example is the scaling group of a locally compact quantum group $mathbb G$ and the fact that the inclusion $C_0(mathbb G) rightarrow L^infty(mathbb G)$ intertwines the relevant scaling groups. Under this general setup, of an inclusion of a $C^*$-algebra into a von Neumann algebra intertwining automorphism groups, we show that the graphs of the analytic generators, despite being only non-self-adjoint operator algebras, satisfy a Kaplansky Density style result. The dual picture is the inclusion $L^1(mathbb G)rightarrow M(mathbb G)$, and we prove an automatic normality result under this general setup. The Kaplansky Density result proves more elusive, as does a general study of quotient spaces, but we make progress under additional hypotheses.
Continuous groups with antilinear operations of the form $G+a_0G$, where $G$ denotes a linear Lie group, and $a_0$ is an antilinear operation which fulfills the condition $a^2_0=pm 1$, were defined and their matrix algebras were investigated in cite{Kocinski4}. In this paper infinitesimal-operator algebras are defined for any group of the form $G+a_0G$, and their properties are determined.
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