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Register a new userOn a possibility to construct gauge invariant quantum formulation for non-gauge classical theory
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A non-gauge dynamical system depending on parameters is considered. It is shown that these parameters can have such values that corresponding canonically quantized theory will be gauge invariant. The equations allowing to find these values of parameters are derived. The prescription under consideration is applied to obtaining the equation of motion for tachyon background field in closed bosonic string theory.
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We propose a method of constructing a gauge invariant canonical formulation for non-gauge classical theory which depends on a set of parameters. Requirement of closure for algebra of operators generating quantum gauge transformations leads to restrictions on parameters of the theory. This approach is then applied for illustration to bosonic string theory coupled to background tachyonic field. It is shown that within the proposed canonical formulation the known mass-shell condition for tachyon is produced.
We consider a general gauge theory with independent generators and study the problem of gauge-invariant deformation of initial gauge-invariant classical action. The problem is formulated in terms of BV-formalism and is reduced to describing the general solution to the classical master equation. We show that such general solution is determined by two arbitrary generating functions of the initial fields. As a result, we construct in explicit form the deformed action and the deformed gauge generators in terms of above functions. We argue that the deformed theory must in general be non-local. The developed deformation procedure is applied to Abelian vector field theory and we show that it allows to derive non-Abelain Yang-Mills theory. This procedure is also applied to free massless integer higher spin field theory and leads to local cubic interaction vertex for such fields.
There exists a well-known duality between the Maxwell-Chern-Simons theory and the self-dual massive model in 2+1 dimensions. This dual description has been extended to topologically massive gauge theories (TMGT) in any dimension. This Letter introduces an unconventional approach to the construction of this type of duality through a reparametrisation of the master theory action. The dual action thereby obtained preserves the same gauge symmetry structure as the original theory. Furthermore, the dual action is factorised into a propagating sector of massive gauge invariant variables and a sector with gauge variant variables defining a pure topological field theory. Combining results obtained within the Lagrangian and Hamiltonian formulations, a new completed structure for a gauge invariant dual factorisation of TMGT is thus achieved.
We formulate the most general gravitational models with constant negative curvature (hyperbolic gravity) on an arbitrary orientable two-dimensional surface of genus $g$ with $b$ circle boundaries in terms of a $text{PSL}(2,mathbb R)_partial$ gauge theory of flat connections. This includes the usual JT gravity with Dirichlet boundary conditions for the dilaton field as a special case. A key ingredient is to realize that the correct gauge group is not the full $text{PSL}(2,mathbb R)$, but a subgroup $text{PSL}(2,mathbb R)_{partial}$ of gauge transformations that go to $text{U}(1)$ local rotations on the boundary. We find four possible classes of boundary conditions, with associated boundary terms, that can be applied to each boundary component independently. Class I has five inequivalent variants, corresponding to geodesic boundaries of fixed length, cusps, conical defects of fixed angle or large cylinder-shaped asymptotic regions with boundaries of fixed lengths and extrinsic curvatures one or greater than one. Class II precisely reproduces the usual JT gravity. In particular, the crucial extrinsic curvature boundary term of the usual second order formulation is automatically generated by the gauge theory boundary term. Class III is a more exotic possibility for which the integrated extrinsic curvature is fixed on the boundary. Class IV is the Legendre transform of class II; the constraint of fixed length is replaced by a boundary cosmological constant term.
We propose a method to compute the scattering angle for classical black hole scattering directly from two massive particle irreducible diagrams in a heavy-mass effective field theory approach to general relativity, without the need of subtracting iteration terms. The amplitudes in this effective theory are constructed using a recently proposed novel colour-kinematic/double copy for tree-level two-scalar, multi-graviton amplitudes, where the BCJ numerators are gauge invariant and local with respect to the massless gravitons. These tree amplitudes, together with graviton tree amplitudes, enter the construction of the required $D$-dimensional loop integrands and allow for a direct extraction of contributions relevant for classical physics. In particular the soft/heavy-mass expansions of full integrands is circumvented, and all iterating contributions can be dropped from the get go. We use this method to compute the scattering angle up to third post-Minkowskian order in four dimensions, including radiation reaction contributions, also providing the expression of the corresponding integrand in $D$ dimensions.
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