Two-form Potential Research Articles

Qualitative analysis of string cosmologies

A qualitative analysis is presented for spatially flat, isotropic and homogeneous cosmologies derived from the string effective action when the combined effects of a dilaton, modulus, two-form potential and central charge deficit are included. The latter has significant effects on the qualitative dynamics. The analysis is also directly applicable to the anisotropic Bianchi type I cosmology.

(p,q)-strings and new spacetime superalgebras

We present a geometric formulation of $(p,q)$-strings in which the $Sl(2;Z)$-doublet of the two-form gauge potentials is constructed as second order in the supersymmetric currents. The currents are constructed using a supergroup manifold corresponding to the $(p,q)$-string superalgebra, which contains fermionic generators in addition to the supercharges and transforms under the $Sl(2;Z)$. The properties of the superalgebra and the generalizations to higher $p$-branes are discussed.

Duality of self-dual actions

Using examples of a D = 2 chiral scalar and a duality-symmetric formulation of D = 4 Maxwell theory we study duality properties of actions for describing chiral bosons. In particular, in the D = 4 case, upon performing a duality transformation of an auxiliary scalar field, which ensures Lorentz covariance of the action, we arrive at a new covariant duality-symmetric Maxwell action, which contains a two-form potential as an auxiliary field. When the two-form field is gauge fixed this action reduces to a duality-symmetric action for Maxwell theory constructed by Zwanziger. We consider properties of this new covariant action and discuss its coupling to external dyonic sources. We also demonstrate that the formulations considered are self-dual with respect to a dualization of the field strengths of the chiral fields.

D = 10, N = IIB supergravity

We present a manifestly Lorentz invariant and supersymmetric component field action for $D = 10$, type $IIB$ supergravity, using a newly developed method for the construction of actions with chiral bosons, which implies only a single scalar non propagating auxiliary field. With the same method we construct also an action in which the complex two-form gauge potential and its Hodge-dual, a complex six-form gauge potential, appear in a symmetric way in compatibility with supersymmetry and Lorentz invariance. The duals of the two physical scalars of the theory turn out to be described by a $SL(2,R)$ triplet of eight-forms whose curvatures are constrained by a single linear relation. We present also a supersymmetric action in which the basic fields and their duals, six-form and eight-form potentials, appear in a symmetric way. All these actions are manifestly invariant under the global $SL(2,R)$-duality group of $D = 10$, $IIB$ supergravity and are equivalent to each other in that their dynamics corresponds to the well known equations of motion of $ D=10$, $IIB$ supergravity.

Vector–Tensor Duality

A dynamical non-Abelian two-form potential gives masses to vector bosons via a topological coupling.1 Unlike in the Abelian case, the two-form cannot be dualized to Goldstone bosons. Duality is restored by coupling a flat connection to the theory in a particular way, and the new action is then dualized to a nonlinear sigma model. The presence of the flat connection is crucial, which saves the original mechanism of Higgs-free topological mass generation from being dualized to a sigma model.

Relationship between the usual formulation of a massless scalar field theory and its formulation in terms of a two-form potential.

We show that the two possible formulations for a divergence- and curl-free vector field, namely, in terms of a scalar or a two-form potential, are equivalent, both as free quantum field theories even in the presence of a background gravitational field and in their coupling to the gravitational field. An apparent disparity in the extrema of the actions in the Euclidean formulations of these theories is resolved by showing that if boundary conditions that are common to the two formulations (which are the only boundary conditions for which the two theories can be compared) are imposed the only extrema of either action has a zero value for the vector field and thus for the stress-energy tensor.

Natural constraints for extended superspace

A simple systematic method to derive superspace constraints is presented. Constraints are given for extended supergravity with one- and two-form gauge potentials in four space-time dimensions. The natural constraints lead to equations of motion forN>4 (supergravity), resp.N>2 (gauge potentials). We discuss modifications for higherN. We also discuss modifications of the field strength of the two-form potential to include Chern-Simons three-forms.

Supergravity in U(1) superspace with a two-form gauge potential

N = 1 supergravity with an antisymmetric tensor gauge potential is formulated in U(1) superspace. This makes the structure of the theory most transparent. Minimal, new minimal, and 16 + 16 supergravity are derived from a reducible 20 + 20 multiplet, and the coupling to supersymmetric gauge theories is constructed. 16 + 16 supergravity can be coupled to gauge fields via the two-form potential in complete analogy to ten-dimensional supergravity.

Gauged seven-dimensional N=2 pure supergravity with two-form potential and its compactifications.

The gauged seven-dimensional N=2 pure supergravity is constructed using differential forms. We use a two-form potential in place of a three-index antisymmetric gauge field carrying the same number of physical degrees of freedom. This theory is compactified into either ${\mathrm{AdS}}^{3}$\ifmmode\times\else\texttimes\fi{}${\mathrm{S}}^{2}$\ifmmode\times\else\texttimes\fi{}${\mathrm{S}}^{2}$ or ${\mathrm{AdS}}^{3}$\ifmmode\times\else\texttimes\fi{}${\mathrm{T}}^{4}$.