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Register a new userConformally Soft Theorem in Gauge Theory
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Asymptotic particle states in four-dimensional celestial scattering amplitudes are labelled by their $SL(2,mathbb{C})$ Lorentz/conformal weights $(h,bar{h})$ rather than the usual energy-momentum four-vector. These boost eigenstates involve a superposition of all energies. As such, celestial gluon (or photon) scattering cannot obey the usual (energetically) soft theorems. In this paper we show that tree-level celestial gluon scattering, in theories with sufficiently soft UV behavior, instead obeys conformally soft theorems involving $h to 0$ or $bar{h} to 0$. Unlike the energetically soft theorem, the conformally soft theorem cannot be derived from low-energy effective field theory.
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Stringent restrictions for model building are imposed by a no-go theorem in noncommutative gauge field theory. Circumventing this theorem is crucial for the construction of realistic models of particle interactions. To this end, the noncommutative construction of tensor representations of gauge groups using half-infinite Wilson lines is extended to allow for gauge groups consisting of an arbitrary number of $U_*(N)$ factors. This as well allows representations other than the ones permitted by the no-go theorem.
We show a sharp conformally invariant gap theorem for Yang-Mills connections in dimension 4 by exploiting an associated Yamabe-type problem.
We present a covariant formulation of the Kinoshita, Lee, Nauenberg (KLN) theorem for processes involving the radiation of soft particles. The role of the disconnected diagrams is explored and a rearrangement of the perturbation theory is performed such that the purely disconnected diagrams are factored out. The remaining effect of the disconnected diagrams results in a simple modification of the usual Feynman rules for the S-matrix elements. As an application, we show that when combined with the Low theorem, this leads to a proof of the absense of the $1/Q$ corrections to inclusive processes (like the Drell-Yan process). In this paper the abelian case is discussed to all orders in the coupling.
Building on the superspace formulation for four-dimensional N=2 matter-coupled supergravity developed in arXiv:0805.4683, we elaborate upon a general setting for field theory in N=2 conformally flat superspaces, and concentrate specifically on the case of anti-de Sitter (AdS) superspace. We demonstrate, in particular, that associated with the N=2 AdS supergeometry is a unique vector multiplet such that the corresponding covariantly chiral field strength W_0 is constant, W_0=1. This multiplet proves to be intrinsic in the sense that it encodes all the information about the N=2 AdS supergeometry in a conformally flat frame. Moreover, it emerges as a building block in the construction of various supersymmetric actions. Such a vector multiplet, which can be identified with one of the two compensators of N=2 supergravity, also naturally occurs for arbitrary conformally flat superspaces. An explicit superspace reduction N=2 to N=1 is performed for the action principle in general conformally flat N=2 backgrounds, and examples of such reduction are given.
Recently it was conjectured that a certain infinite-dimensional diagonal subgroup of BMS supertranslations acting on past and future null infinity (${mathscr I}^-$ and ${mathscr I}^+$) is an exact symmetry of the quantum gravity ${cal S}$-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinbergs soft graviton theorem. Along the way we construct the canonical generators of supertranslations at ${mathscr I}^pm$, including the relevant soft graviton contributions. Boundary conditions at the past and future of ${mathscr I}^pm$ and a correspondingly modified Dirac bracket are required. The soft gravitons enter as boundary modes and are manifestly the Goldstone bosons of spontaneously broken supertranslation invariance.
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