Komar integral and Smarr formula for axion-dilaton black holes versus S duality

We construct the Komar integral for axion-dilaton gravity using Wald’s formalism and momentum maps and we use it to derive a Smarr relation for stationary axion-dilaton black holes. While the Wald-Noether 2-form charge is not invariant under SL(2, ℝ) electric-magnetic duality transformations because Wald’s formalism does not account for magnetic charges and potentials, the Komar integral constructed with it turns out to be invariant and, in more general theories, it will be fully symplectic invariant. We check the Smarr formula obtained with the most general family of static axion-dilaton black holes.

On the partial breaking of $\mathcal{N}=2$ rigid supersymmetry with a complex hypermultiplet

We study partial supersymmetry breaking in effective $\mathcal{N}=2$ U$ \left( 1\right) ^{n}$ gauge theory coupled to complex hypermultiplets by using the method of L. Andrianopoli et al., Phys. Lett. B 744, 116 (2015), which we refer to as the ADFT method. We derive the generalization of the symplectic invariant ADFT formula $\zeta _{a}=\frac{1}{2}\varepsilon _{abc}(\mathcal{P}^{bM}\mathcal{C}_{MN}\mathcal{P}^{cN}) $, capturing information on partial breaking. Our extension of this anomaly is expressed as $d_{a}=\frac{1}{2}\varepsilon _{abc}\mathbb{P}^{bM}\mathcal{C}_{MN}\mathbb{P}^{cN}+\mathcal{J}_{a}$. The generalized moment maps $\mathbb{P}^{aM}$ contain $\mathcal{P}^{aM}$ and also depend on electric/magnetic coupling charges $G^{M}=( \eta ^{i},g_{i}) $; the $\mathcal{J}_{a}$ is an extra contribution induced by Killing isometries in the complex hypermatter sector. Using SP$\left(2n,\mathbb{R}\right)$ symplectic symmetry, we also give the $\mathcal{N}=2$ partial breaking condition and derive the model of I. Antoniadis et al., Nucl. Phys. B 863, 471 (2012) by a particular realization of the $d_{a}$ anomaly.

Families of(1,2)-symplectic metrics on full flag manifolds

We obtain new families of(1,2)-symplectic invariant metrics on the full complex flag manifoldsF(n). Forn≥5, we characterizen−3differentn-dimensional families of(1,2)-symplectic invariant metrics onF(n). Each of these families corresponds to a different class of nonintegrable invariant almost complex structures onF(n).

Symplectic displacement energy for Lagrangian submanifolds

Recently H. Hofer defined a new symplectic invariant which has a beautiful dynamical meaning. In the present paper we study this invariant for Lagrangian submanifolds of symplectic manifolds. Our approach is based on Gromov's theory of pseudo-holomorphic curves.

ON THE SYMPLECTIC STRUCTURE OF HARMONIC SUPERSPACE

The symplectic properties of harmonic superspace are studied. It is shown that Diff (S2) is isomorphic to Diff 0(S3)/ Ab(Diff 0(S3)), where Diff 0(S3) is the group of the diffeomorphisms of S3 preserving the Cartan charge operator D0 and Ab (Diff0(S3)) is its Abelian subgroup generated by the Cartan vectors L0=w0D0. We show also that the eigenvalue equation D0λ(z)=0 defines a symplectic structure in harmonic superspace, and we calculate the corresponding algebra. The general symplectic invariant coupling of the Maxwell prepotential is constructed in both flat and curved harmonic superspace. Other features are discussed.