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We propose novel asymptotically locally flat boundary conditions for Einstein Gravity without cosmological constant in four dimensions that are consistent with the variational principle. They allow for complex solutions that are asymptotically diffeomorphic to flat space-times under complexified diffeomorphisms. We show that the resultant asymptotic symmetries are an extension of the Poincare algebra to a copy of Virasoro, a chiral $mathfrak{sl}(2,{mathbb C})$ current algebra along with two chiral $mathfrak{u}(1)$ currents. We posit that these bulk symmetries are direct analogues of the recently discovered chiral algebra symmetries of gravitational scattering amplitudes as celestial CFT correlation functions.
From pure Yang-Mills action for the $SL(5,mathbb{R})$ group in four Euclidean dimensions we obtain a gravity theory in the first order formalism. Besides the Einstein-Hilbert term, the effective gravity has a cosmological constant term, a curvature s
We provide a set of chiral boundary conditions for three-dimensional gravity that allow for asymptotic symmetries identical to those of two-dimensional induced gravity in light-cone gauge considered by Polyakov. These are the most general boundary co
Generalizations of the AGT correspondence between 4D $mathcal{N}=2$ $SU(2)$ supersymmetric gauge theory on ${mathbb {C}}^2$ with $Omega$-deformation and 2D Liouville conformal field theory include a correspondence between 4D $mathcal{N}=2$ $SU(N)$ su
Using representation theory, we compute the spectrum of the Dirac operator on the universal covering group of $SL_2(mathbb R)$, exhibiting it as the generator of $KK^1(mathbb C, mathfrak A)$, where $mathfrak A$ is the reduced $C^*$-algebra of the gro
We study confining strings in ${cal{N}}=1$ supersymmetric $SU(N_c)$ Yang-Mills theory in the semiclassical regime on $mathbb{R}^{1,2} times mathbb{S}^1$. Static quarks are expected to be confined by double strings composed of two domain walls - which