Couplings Of Vector Multiplets Research Articles

Shifts of prepotentials (with an appendix by Michele Vergne)

We study the dynamics of supersymmetric theories in five dimensions obtained by compactifications of M-theory on a Calabi-Yau threefold X. For a compact X, this is determined by the geometry of X, in particular the Kähler class dependence of the volume of X determines the effective couplings of vector multiplets. Rigid supersymmetry emerges in the limit of divergent volume, prompting the study of the structure of Duistermaat-Heckman formula and its generalizations for non-compact toric Kähler manifolds. Our main tool is the set of finite-difference equations obeyed by equivariant volumes and their quantum versions. We also discuss a physical application of these equations in the context of seven-dimensional gauge theories, extending and clarifying our previous results. The appendix by M. Vergne provides an alternative local proof of the shift equation.

Alternative N=2 supergravity in five dimensions with singularities

We present an alternative N=2 supergravity multiplet coupled to n copies of vector multiplets and n′ copies of hypermultiplets in five dimensions. Our supergravity multiplet contains a single antisymmetric tensor and a dilaton, which are natural Neveu–Schwarz massless fields in superstring theory. The absence of the explicit Chern–Simons terms in our Lagrangian deletes the non-trivial constraints on the couplings of vector multiplets in the conventional formulation. The scalars in the vector multiplets form the σ-model for the coset SO( n,1)/ SO( n), like those in the vector multiplets coupled to N=1 supergravity in nine dimensions, while the scalars in the hypermultiplets form that for the quaternionic Kähler manifold Sp( n′,1)/ Sp( n′)× Sp(1). We also perform the gauging of the SO(2) subgroup of the Sp(1)=SL(2, R) automorphism group of N=2 supersymmetry. Our result is also generalized to singular 5D space–time as in the conventional formulation, as a preliminary for supersymmetric Randall–Sundrum brane world scenario.

A symplectic covariant formulation of special Kähler geometry in superconformal calculus

We present a formulation of the coupling of vector multiplets to N = 2 supergravity which is symplectic covariant (and thus is not based on a prepotential) and uses superconformal tensor calculus. We do not start from an action, but from the combination of the generalized Bianchi identities of the vector multiplets in superspace, a symplectic definition of special Kähler geometry, and the supersymmetric partners of the corresponding constraints. These involve the breaking to super-Poincaré symmetry, and lead to on-shell vector multiplets. This symplectic approach gives the framework to formulate vector multiplet couplings using a weaker defining constraint for special Kähler geometry, which is an extension of older definitions of special Kähler manifolds for some cases with only one vector multiplet.

N=2 Electric-magnetic duality in a chiral background

We establish the consistency of duality transformations for generic systems of $N=2$ vector supermultiplets in the presence of a chiral background field. This is relevant, for instance, when dealing with spurion fields or when considering higher-derivative couplings of vector multiplets to supergravity. We point out that under duality most quantities do not transform as functions. With few exceptions, true functions are nonholomorphic, even though the duality transformations themselves are holomorphic in nature.

Special geometry and symplectic transformations

Special Kahler manifolds are defined by coupling of vector multiplets to $N=2$ supergravity. The coupling in rigid supersymmetry exhibits similar features. These models contain $n$ vectors in rigid supersymmetry and $n+1$ in supergravity, and $n$ complex scalars. Apart from exceptional cases they are defined by a holomorphic function of the scalars. For supergravity this function is homogeneous of second degree in an $(n+1)$-dimensional projective space. Another formulation exists which does not start from this function, but from a symplectic $(2n)$- or $(2n+2)$-dimensional complex space. Symplectic transformations lead either to isometries on the manifold or to symplectic reparametrizations. Finally we touch on the connection with special quaternionic and very special real manifolds, and the classification of homogeneous special manifolds.

String-dual F1-function in the three parameter model

The computation of the holomorphic F 1-function describing one-loop gravitational couplings of vectormultiplets is shown to confirm the string-string duality of the proposed dual pair consisting of the heterotic string on K3 × T 2 with gauge group U(1) 4 and the type IIA string on the Calabi-Yau WP 1,1,2,8,12 4(24).

Perturbative couplings of vector multiplets in N = 2 heterotic string vacua

We study the low-energy effective Lagrangian of N = 2 heterotic string vacua at the classical and quantum level. The couplings of the vector multiplets are uniquely determined at the tree level, while the loop corrections are severely constrained by the exact discrete symmetries of the string vacuum. We evaluate the general transformation law of the perturbative prepotential and determine its form for the toroidal compactifications of six-dimensional N = 1 supersymmetric vacua.

Topological twist in four dimensions, R-duality and hyperinstantons

In this paper we continue the programme of topologically twisting N = 2 theories in D = 4, focusing on the coupling of vector multiplets to N = 2 supergravity. We show that in the minimal case, namely when the special geometry prepotential F( X) is a quadratic polynomial, the theory has a so far unknown on-shell U(1) symmetry, that we name R-duality. R-duality is a generalization of the chiral-dual on-shell symmetry of N = 2 pure supergravity and of the R-symmetry of N = 2 super Yang-Mills theory. Thanks to this, the theory can be topologically twisted and topologically shifted, precisely as pure N = 2 supergravity, to yield a natural coupling of topological gravity to topological Yang-Mills theory. The gauge-fixing condition that emerges from the twisting is the self-duality condition on the gauge field strength and on the spin connection. Hence our theory reduces to intersection theory in the moduli-space of gauge instantons living in gravitational instanton backgrounds. We remark that, for deep properties of the parent N = 2 theory, the topological Yang-Mills theory we obtain by taking the flat space limit of our gravity-coupled lagrangian is different from the Donaldson theory constructed by Witten. Whether this difference is substantial and what its geometrical implications may be is yet to be seen. We also discuss the topological twist of the hypermultiplets leading to topological quaternionic sigma-models. The instantons of these models, named by us hyperinstantons, corespond to a notion of triholomorphic mappings discussed in the paper. In all cases the new ghost number is the sum of the old ghost number plus the R-duality charge. The observables described by the theory are briefly discussed. In conclusion, the topological twist of the complete N = 2 theory defines intersection theory in the moduli-space of gauge instantons plus gravitational instantons plus hyperinstantons. This is possibly a new subject for further mathematical investigation.

Potentials and symmetries of general gauged N = 2 supergravity-Yang-Mills models

The general couplings of vector multiplets to N = 2 supergravity are presented. The possibility of generalized duality invariance of the bosonic field equations is investigated. Various ways to gauge N = 2 supergravity are explored. Special attention is given to the case of one vector multiplet; for minimal coupling there are only three inequivalent potentials which coincide with the potentials of gauged N = 4 supergravity.