Infinite-Dimensional Algebras as Extensions of Kinematic Algebras by Joaquim Gomis, Axel Kleinschmidt, Axel Kleinschmidt

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CFT/gravity correspondence on the isolated horizon by Amit Ghosh, Daniele Pranzetti

“…We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localised at the horizon which satisfy a Kac–Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational flux degrees of freedom in terms of the zero modes of the Kac–Moody algebra defined on the boundary of a punctured disk. …”
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Kac's conjecture from Nakajima quiver varieties by Hausel, T

“…In particular this implies that the constant term of the polynomial counting the number of absolutely indecomposable representations of a quiver equals the multiplicity of a a certain weight in the corresponding Kac-Moody algebra, which was conjectured by Kac in 1982.…”

The Beilinson-Bernstein localization theorem for the affine Grassmannian by Fortuna, Giorgia

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Holographic entanglement entropy in AdS3/WCFT by Baizhi Gao, Jianfei Xu

“…In this paper, we consider AdS3 with Compère-Song-Strominger (CSS) boundary conditions, under which the dual field theory is warped conformal field theory (WCFT), featuring a Virasoro-Kac-Moody algebra. We provide a holographic dual picture of the single interval entanglement entropy in WCFT in the bulk AdS3. …”
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Extended geometries by Martin Cederwall, Jakob Palmkvist

“…Abstract We present a unified and completely general formulation of extended geometry, characterised by a Kac-Moody algebra and a highest weight coordinate module. …”
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Warped conformal symmetries of the accelerating Kerr black hole by Jianfei Xu

“…By invoking a set of non-trivial diffeomorphisms near the horizon bifurcation surface of the accelerating Kerr black hole, the Dirac brackets among charges of the diffeomorphisms form the symmetry algebra of a warped CFT which consists of one Virasoro and one Kac-Moody algebra with central extensions. This provides the evidence for warped CFTs being possible holographic dual to accelerating Kerr black holes. …”
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Warped symmetries of the Kerr black hole by Ankit Aggarwal, Alejandra Castro, Stéphane Detournay

“…Our gravitational charges are organized into a Virasoro-Kac-Moody algebra with non-trivial central extensions. …”
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Infinite pseudo-conformal symmetries of classical $T \bar T$, $J \bar T $ and $J T_a$ - deformed CFTs by Monica Guica, Ruben Monten

“…In the case of the $J \bar T$ and $J T_a$ deformations, we find two copies of a functional Witt - Kac-Moody algebra. In the case of the $T \bar T$ deformation, we show that it is also possible to obtain two commuting copies of the Witt algebra.…”
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From Moyal deformations to chiral higher-spin theories and to celestial algebras by Ricardo Monteiro

“…Regarding celestial holography, the Moyal deformation of self-dual gravity was recently shown to lead to the loop algebra of W ∧, and we obtain here the analogous deformation of a Kac-Moody algebra corresponding to Moyal-deformed self-dual Yang-Mills theory. …”
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Galilean free Lie algebras by Joaquim Gomis, Axel Kleinschmidt, Jakob Palmkvist

“…We show how various extensions of the ordinary Galilei algebra can be obtained by truncations and contractions, in some cases via an affine Kac-Moody algebra. The infinite-dimensional Lie algebras could be useful in the construction of generalized Newton-Cartan theories gravity theories and the objects that couple to them.…”
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Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory by Bertolini, E, Gambuti, G, Maggiore, N

“…As in the flat bulk case with planar boundary, we find that also on the radial boundary of a curved background a Kaç-Moody algebra exists, with the same central charge as in the flat case, which henceforth depends neither on the bulk metric nor on the geometry of the boundary. …”

Generalised holonomies and K(E 9) by Axel Kleinschmidt, Hermann Nicolai

“…Abstract The involutory subalgebra K( e $$ \mathfrak{e} $$ 9) of the affine Kac-Moody algebra e $$ \mathfrak{e} $$ 9 was recently shown to admit an infinite sequence of unfaithful representations of ever increasing dimensions [1]. …”
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Holographic Projection of Electromagnetic Maxwell Theory by Erica Bertolini, Nicola Maggiore

“…As a consequence of the presence of the boundary, two broken Ward identities are recovered, which, on-shell, give rise to two conserved currents living on the edge. A Kaç-Moody algebra formed by a subset of the bulk fields is obtained with central charge proportional to the inverse of the Maxwell coupling constant, and the degrees of freedom of the boundary theory are identified as two vector fields, also suggesting that the 3D theory should be a gauge theory. …”
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Correlation functions of warped CFT by Wei Song, Jianfei Xu

“…Abstract Warped conformal field theory (WCFT) is a two dimensional quantum field theory whose local symmetry algebra consists of a Virasoro algebra and a U(1) Kac-Moody algebra. In this paper, we study correlation functions for primary operators in WCFT. …”
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Goldstone modes and photonization for higher form symmetries by Diego M. Hofman, Nabil Iqbal

“…The charges are shown to obey an algebra with central extension, which is an analogue of the 2d Abelian Kac-Moody algebra for higher form symmetries.…”
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Celestial Yang-Mills amplitudes and D = 4 conformal blocks by Wei Fan, Angelos Fotopoulos, Stephan Stieberger, Tomasz R. Taylor, Bin Zhu

“…The current factor is given by the group-dependent part of the Wess-Zumino-Witten correlator of four holomorphic currents with a non-vanishing level of Kač-Moody algebra. The scalar factor can be expressed in terms of a complex integral of the Koba-Nielsen form, similar to the integrals describing four-point correlators in Coulomb gas models and, more generally, in the infinite central charge limit of Liouville theory. …”
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Asymptotic symmetries of colored gravity in three dimensions by Euihun Joung, Jaewon Kim, Jihun Kim, Soo-Jong Rey

“…The resulting asymptotic symmetry algebra is a nonlinear extension of s u N ^ $$ \widehat{\mathfrak{su}(N)} $$ Kac-Moody algebra, supplemented by additional generators corresponding to the massless spin-two adjoint matter fields.…”
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Macdonald index and chiral algebra by Jaewon Song

“…We test this prescription for the Argyres-Douglas theories of type (A 1 , A 2n ) and (A 1 , D 2n+1) where the chiral algebras are given by Virasoro and s u ^ 2 $$ \widehat{\mathfrak{su}}(2) $$ affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.…”
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On Sugawara construction on celestial sphere by Wei Fan, Angelos Fotopoulos, Stephan Stieberger, Tomasz R. Taylor

“…Abstract Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. …”
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