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Register a new userA note on Faddeev--Popov action for doubled-yet-gauged particle and graded Poisson geometry
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The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point. In this note, we consider a doubled and at the same time gauged particle action, and show that its BRST formulation including Faddeev--Popov ghosts matches with the graded Poisson geometry that has been recently used to describe the symmetries of Double Field Theory. Besides, by requiring target spacetime diffeomorphisms at the quantum level, we derive quantum corrections to the classical action involving dilaton, which might be comparable with the Fradkin--Tseytlin term on string worldsheet.
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We construct a world-sheet action for Green-Schwarz superstring in terms of doubled-yet-gauged spacetime coordinates. For an arbitrarily curved NS-NS background, the action possesses $mathbf{O}(10,10)$ T-duality, $mathbf{Spin}(1,9)timesmathbf{Spin}(9,1)$ Lorentz symmetry, coordinate gauge symmetry, spacetime doubled-yet-gauged diffeomorphisms, world-sheet diffeomorphisms and Weyl symmetry. Further, restricted to flat backgrounds, it enjoys maximal spacetime supersymmetry and kappa-symmetry. After the auxiliary coordinate gauge symmetry potential being integrated out, our action can consistently reduce to the original undoubled Green-Schwarz action. Thanks to the twofold spin groups, the action is unique: it is specific choices of the NS-NS backgrounds that distinguish IIA or IIB, as well as lead to non-Riemannian or non-relativistic superstring a la Gomis-Ooguri which might deserve the nomenclature, type IIC.
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Recent works have revealed that the recipe for field-antifield quantization of Lagrangian gauge theories can be considerably relaxed when it comes to choosing a path integral measure rho if a zero-order term u_{rho} is added to the Delta operator. The effects of this odd scalar term u_{rho} become relevant at two-loop order. We prove that u_{rho} is essentially the odd scalar curvature of an arbitrary torsion-free connection that is compatible with both the anti-Poisson structure E and the density rho. This extends a previous result for non-degenerate antisymplectic manifolds to degenerate anti-Poisson manifolds that admit a compatible two-form.
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We consider gauged skyrmions with boundary conditions which break the gauge from $mathrm{SU}(2)$ to $mathrm{U}(1)$ in models derived from Yang-Mills theory. After deriving general topological energy bounds, we approximate charge $1$ energy minimisers using KvBLL calorons with non-trivial asymptotic holonomy, use them to calibrate the model to optimise the ratio of energy to lower bound, and compare them with solutions to full numerical simulation. Skyrmions from calorons with non-trivial asymptotic holonomy exhibit a non-zero magnetic dipole moment, which we calculate explicitly, and compare with experimental values for the proton and the neutron. We thus propose a way to develop a physically realistic Skyrme-Maxwell theory, with the potential for exhibiting low binding energies.
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