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Register a new userNo-go for Partially Massless Spin-2 Yang-Mills
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There are various no-go results forbidding self-interactions for a single partially massless spin-2 field. Given the photon-like structure of the linear partially massless field, it is natural to ask whether a multiplet of such fields can interact under an internal Yang-Mills like extension of the partially massless symmetry. We give two arguments that such a partially massless Yang-Mills theory does not exist. The first is that there is no Yang-Mills like non-abelian deformation of the partially massless symmetry, and the second is that cubic vertices with the appropriate structure constants do not exist.
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We provide a systematic and comprehensive derivation of the linearized dynamics of massive and partially massless spin-2 particles in a Schwarzschild (anti) de Sitter black hole background, in four and higher spacetime dimensions. In particular, we show how to obtain the quadratic actions for the propagating modes and recast the resulting equations of motion in a Schrodinger-like form. In the case of partially massless fields in Schwarzschild de Sitter spacetime, we study the isospectrality between modes of different parity. In particular, we prove isospectrality analytically for modes with multipole number $L=1$ in four spacetime dimensions, providing the explicit form of the underlying symmetry. We show that isospectrality between partially massless modes of different parity is broken in higher-dimensional Schwarzschild de Sitter spacetimes.
We revisit the problem of building consistent interactions for a multiplet of partially massless spin-2 fields in (anti-)de Sitter space. After rederiving and strengthening the existing no-go result on the impossibility of Yang-Mills type non-abelian deformations of the partially massless gauge algebra, we prove the uniqueness of the cubic interaction vertex and field-dependent gauge transformation that generalize the structures known from single-field analyses and in four spacetime dimensions, where our results also hold. Unlike in the case of one partially massless field, however, we show that for two or more particle species the cubic deformations can be made consistent at the complete non-linear level, albeit at the expense of allowing for negative relative signs between kinetic terms, making our new theory akin to conformal gravity. Our construction thus provides the first example of an interacting theory containing only partially massless fields.
Various gauge invariant but non-Yang-Mills dynamical models are discussed: Precis of Chern-Simons theory in (2+1)-dimensions and reduction to (1+1)-dimensional B-F theories; gauge theories for (1+1)-dimensional gravity-matter interactions; parity and gauge invariant mass term in (2+1)-dimensions.
We study the empirical realisation of the memory effect in Yang-Mills theory, especially in view of the classical vs. quantum nature of the theory. Gauge invariant analysis of memory in classical U(1) electrodynamics and its observation by total change of transverse momentum of a charge is reviewed. Gauge fixing leads to a determination of a gauge transformation at infinity. An example of Yang-Mills memory then is obtained by reinterpreting known results on interactions of a quark and a large high energy nucleus in the theory of Color Glass Condensate. The memory signal is again a kick in transverse momentum, but it is only obtained in quantum theory after fixing the gauge, after summing over an ensemble of classical processes.
By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincare. As a concrete example we focus on the new-minimal (12+12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell Yang-Mills multiplets (4+4,N_L =1)and(3+0,N_R =0).
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