Virasoro algebra from harmonic superspace

Abstract

Using harmonic superspace techniques we construct a new field realization of the Virasoro algebra. The main conformal objects are U(1) Cartan tensors instead of the U(1) Lorentz ones. The new conformal model, which admits moreover a d = 2 (4,O) global supersymmetry, is constructed out of the infinitely relaxed Howe-Stelle-Townsend and Fayet-Sohnius hypermultiplets. The conformal current T4+ together with the harmonic superspace operator product expansion rules are given. The Virasoro algebra and the harmonic superspace Schwarzian derivative S4+ are also derived.PACS number(s): 1 1.30.Pb, 02.20. + b

Centrally extended BMS4 Lie algebroid

“…Note that one could also have worked with appropriate distributions directly on the celestial sphere (see e.g. [48,49,50,51,52,53]). The point of view taken here consists in first using transformation rules and invariance properties of various quantities such as the Bondi mass aspect under conformal rescalings [54,55] to transpose everything to the Riemann sphere before considering distributions.…”

BMS charge algebra

“…A way to make sense of the divergent integrals could be to use the theory of harmonic variables and distributions on the sphere introduced in the context of harmonic superspace [29] (see also [30] for a review) and applied to local conformal properties of the sphere in [31,32]. It would mean to probe solution space through objects such as…”

On matrix model compactification on non-commutative F 0 geometry

“…The second thing is that the compactified IKKT coordinates X i are either U(1) × U(1) gauge-covariant derivatives for λ = 1 or operators obeying a Heisenberg algebra for λ = 1 as described by equations ( 15), ( 17) and (19). We will show in the remainder of this paper that these features are grosso modo valid also for the case of F θ geometry.…”

“…We have not given details concerning the compactification on local F 0 ; nevertheless, preliminary results of the compactification of matrix models on local F 0 and more generally on local F n may already be written down. They may be read from the analysis of the present paper by using the correspondence given in [19] and results of [17,20].…”