10 research outputs found
Supersymmetric electric-magnetic duality of hypergravity
Hypergravity is the theory in which the graviton, of spin-2, has a
supersymmetric partner of spin-5/2. There are "no-go" theorems that prevent
interactions in these higher spin theories. However, it appears that one can
circumvent them by bringing in an infinite tower of higher spin fields. With
this possibility in mind, we study herein the electric-magnetic duality
invariance of hypergravity. The analysis is carried out in detail for the free
theory of the spin-(2,5/2) multiplet, and it is indicated how it may be
extended to the infinite tower of higher spins. Interactions are not
considered. The procedure is the same that was employed recently for the
spin-(3/2,2) multiplet of supergravity. One introduces new potentials
("prepotentials") by solving the constraints of the Hamiltonian formulation. In
terms of the prepotentials, the action is written in a form in which its
electric-magnetic duality invariance is manifest. The prepotential action is
local, but the spacetime invariance is not manifest. Just as for the spin-2 and
spin-(3/2,2) cases, the gauge symmetries of the prepotential action take a form
similar to those of the free conformal theory of the same multiplet. The
automatic emergence of gauge conformal invariance out of demand of manifest
duality invariance, is yet another evidence of the subtle interplay between
duality invariance and spacetime symmetry. We also compare and contrast the
formulation with that of the analogous spin-(1,3/2) multiplet
Spacetime as a quantum circuit
We propose that finite cutoff regions of holographic spacetimes represent
quantum circuits that map between boundary states at different times and
Wilsonian cutoffs, and that the complexity of those quantum circuits is given
by the gravitational action. The optimal circuit minimizes the gravitational
action. This is a generalization of both the "complexity equals volume"
conjecture to unoptimized circuits, and path integral optimization to finite
cutoffs. Using tools from holographic , we find that surfaces of
constant scalar curvature play a special role in optimizing quantum circuits.
We also find an interesting connection of our proposal to kinematic space, and
discuss possible circuit representations and gate counting interpretations of
the gravitational action.Comment: 26 pages, 2 figure
Cost of holographic path integrals
We consider proposals for the cost of holographic path integrals.
Gravitational path integrals within finite radial cutoff surfaces have a
precise map to path integrals in deformed holographic CFTs. In
Nielsen's geometric formulation cost is the length of a
not-necessarily-geodesic path in a metric space of operators. Our cost
proposals differ from holographic state complexity proposals in that (1) the
boundary dual is cost, a quantity that can be `optimised' to state complexity,
(2) the set of proposals is large: all functions on all bulk subregions of any
co-dimension which satisfy the physical properties of cost, and (3) the
proposals are by construction UV-finite. The optimal path integral that
prepares a given state is that with minimal cost, and cost proposals which
reduce to the CV and CV2.0 complexity conjectures when the path integral is
optimised are found, while bounded cost proposals based on gravitational action
are not found. Related to our analysis of gravitational action-based proposals,
we study bulk hypersurfaces with a constant intrinsic curvature of a specific
value and give a Lorentzian version of the Gauss-Bonnet theorem valid in the
presence of conical singularities.Comment: 52 pages + appendices, 14 figures; v2 references adde
Twisted self-duality for higher spin gauge fields and prepotentials
We show that the equations of motion for (free) integer higher spin gauge fields can be formulated as twisted self-duality conditions on the higher spin curvatures of the spin-s field and its dual. We focus on the case of four spacetime dimensions, but formulate our results in a manner applicable to higher spacetime dimensions. The twisted self-duality conditions are redundant and we exhibit a nonredundant subset of conditions, which have the remarkable property to involve only first-order derivatives with respect to time. This nonredundant subset equates the electric field of the spin-s field (which we define) to the magnetic field of its dual (which we also define), and vice versa. The nonredundant subset of twisted self-duality conditions involve the purely spatial components of the spin-s field and its dual, and also the components of the fields with one zero index. One can get rid of these gauge components by taking the curl of the equations, which does not change their physical content. In this form, the twisted self-duality conditions can be derived from a variational principle that involves prepotentials. These prepotentials are the higher spin generalizations of the prepotentials previously found in the spins 2 and 3 cases. The prepotentials have again the intriguing feature of possessing both higher spin diffeomorphism invariance and higher spin conformal geometry. The tools introduced in an earlier paper for handling higher spin conformal geometry turn out to be crucial for streamlining the analysis. In four spacetime dimensions where the electric and magnetic fields are tensor fields of the same type, the twisted self-duality conditions enjoy an SO(2) electric-magnetic invariance. We explicitly show that this symmetry is an "off-shell symmetry" (i.e. a symmetry of the action and not just of the equations of motion). Remarks on the extension to higher dimensions are given.SCOPUS: ar.jinfo:eu-repo/semantics/publishe