A double copy for asymptotic symmetries in the self-dual sector

We give a double copy construction for the symmetries of the self-dual sectors of Yang-Mills (YM) and gravity, in the light-cone formulation. We find an infinite set of double copy constructible symmetries. We focus on two families which correspond to the residual diffeomorphisms on the gravitational side. For the first one, we find novel non-perturbative double copy rules in the bulk. The second family has a more striking structure, as a non-perturbative gravitational symmetry is obtained from a perturbatively defined symmetry on the YM side.At null infinity, we find the YM origin of the subset of extended Bondi-Metzner-Sachs (BMS) symmetries that preserve the self-duality condition. In particular, holomorphic large gauge YM symmetries are double copied to holomorphic supertranslations. We also identify the single copy of superrotations with certain non-gauge YM transformations that to our knowledge have not been previously presented in the literature.

ENHANCED DUALITY SYMMETRIES FOR A PAIR OF DIRAC–BORN–INFELD ACTIONS

We consider a total action composed of two Dirac–Born–Infeld (DBI) actions: one for a vector field Aμ and another for an axial vector field Bμ. We impose a duality condition [Formula: see text], where [Formula: see text] is the Hodge dual of Gμν, and g is a DBI interaction constant. Interestingly, there are two different global duality rotation symmetries in the presence of DBI interactions: (i) [Formula: see text], [Formula: see text], and (ii) δζAμ = - ζBμ, δζBμ = + ζAμ. Both of these symmetry are on-shell symmetries, including nonlinear higher-order terms. The remarkable aspect is that these symmetries are valid even in the presence of DBI interactions. The coupling of this system to N = 1 supergravity is also discussed.

NONLINEAR REALIZATION OF THE $\mathcal{N}=2$, D = 6 SUPERGRAVITY

We have applied the method of dualization to construct the coset realization of the bosonic sector of the [Formula: see text], D = 6 supergravity which is coupled to a tensor multiplet. The bosonic field equations are regained through the Cartan–Maurer equation which the Cartan form satisfies. The first-order formulation of the theory is also obtained as a twisted self-duality condition within the nonlinear coset construction.

FUZZY INSTANTONS

We present a series of instanton-like solutions to a matrix model which satisfy a self-duality condition and possess an action whose value is, to within a fixed constant factor, an integer l2. For small values of the dimension n2 of the matrix algebra the integer resembles the result of a quantization condition but as n → ∞ the ratio l/n can tend to an arbitrary real number between zero and one.

GRAVITATIONAL INSTANTONS IN ASHTEKAR’S FORMALISM

Gravitational instantons of Bianchi type IX space are constructed in Ashtekar’s canonical formalism. Instead of solving the self-duality condition, we fully solve the constraint on the “initial surface” and “Hamiltonian equations.” This formalism is applicable to the matter coupled system with cosmological constant.

DAVEY-STEWARTSON EQUATION FROM A ZERO CURVATURE AND A SELF-DUALITY CONDITION

We derive the two equations of Davey-Stewartson type from a zero curvature condition associated with SL(2, ℝ) in (2+1) dimensions. We show in general how a (2+1)dimensional zero curvature condition can be obtained from the self-duality condition in (3+3) dimensions and show in particular how the Davey-Stewartson equations can be obtained from the self-duality condition associated with SL(2, ℝ) in (3+3) dimensions.

SELF-DUALITY AND THE SUPERSYMMETRIC KdV HIERARCHY

We show how the supersymmetric KdV equation can be obtained from the self-duality condition on Yang-Mills fields in four dimensions associated with the graded Lie algebra OSp(2/1). We also obtain the hierarchy of SUSY KdV equations as well as the s-KdV equations from such a condition. We formulate the SUSY KdV hierarchy as a vanishing curvature condition associated with the U(1) group and show how an Abelian self-duality condition in four dimensions can also lead to these equations.

THE COMPLETE SUPERSPACE ACTION OF CHIRAL D=10, N=2 SUPERGRAVITY

We construct the complete superspace action ℒ of chiral D=10, N=2 supergravity. The self-duality condition on the field strength Fa1 - a5 is derived as an equation of motion in superspace. The space-time restriction of ℒ is not supersymmetric, since the self-duality condition does not follow from the space-time variational equations. However, supersymmetry can be restored via the introduction of a Lagrange multiplier term.