Massive P-forms Research Articles

P-form electrodynamics as edge modes of a topological field theory

p-form electrodynamics in d ≥ 2 dimensions is shown to emerge as the edge modes of a topological field theory with a precise set of boundary conditions, through the Hamiltonian reduction of its action. Electric and magnetic charges correspond to Noether ones in the topological field theory. For chiral p-forms, the topological action can be consistently truncated, so that the Henneaux-Teitelboim action is recovered from a pure Chern-Simons theory, with a manifestly covariant stress-energy tensor at the boundary. Topologically massive p-form electrodynamics as well as axion couplings are also shown to be described through this mechanism by considering suitable (self-)interaction terms in the topological theory.

Effective actions for dual massive (super) p-forms

In d dimensions, the model for a massless p-form in curved space is known to be a reducible gauge theory for p > 1, and therefore its covariant quantisation cannot be carried out using the standard Faddeev-Popov scheme. However, adding a mass term and also introducing a Stueckelberg reformulation of the resulting p-form model, one ends up with an irreducible gauge theory which can be quantised à la Faddeev and Popov. We derive a compact expression for the massive p-form effective action, {Gamma}_p^{(m)} , in terms of the functional determinants of Hodge-de Rham operators. We then show that the effective actions {Gamma}_p^{(m)} and {Gamma}_{d-p-1}^{(m)} differ by a topological invariant. This is a generalisation of the known result in the massless case that the effective actions Γp and Γd−p−2 coincide modulo a topological term. Finally, our analysis is extended to the case of massive super p-forms coupled to background mathcal{N} = 1 supergravity in four dimensions. Specifically, we study the quantum dynamics of the following massive super p-forms: (i) vector multiplet; (ii) tensor multiplet; and (iii) three-form multiplet. It is demonstrated that the effective actions of the massive vector and tensor multiplets coincide. The effective action of the massive three-form is shown to be a sum of those corresponding to two massive scalar multiplets, modulo a topological term.

A Note On The First Class Approaches Of Massive P-Forms

Abstract The problem of quantization of the massive p-forms is considered in the framework of the Batalin-Fradkin (BF) approach based on path integral. The quantization procedure relies on the path integral of a first-class system equivalent with the original theory. This first-class system is constructed using the BF method.

MASSIVE p-FORMS: FIRST-CLASS APPROACHES

Massive p-forms are analyzed from the point of view of the Hamiltonian path integral quantization. More precisely, the quantization procedure is based on the path integral of a first-class system equivalent (at both classical and quantum levels) with the original theory. This first-class system is constructed using the gauge unfixing approach and the Batalin–Fradkin method, respectively. Both methods finally output the manifestly Lorentz covariant path integral for p- and (D-p-1)-forms with topological coupling or (p-1)- and p-forms with Stückelberg coupling.

Worldline approach to vector and antisymmetric tensor fields II

We extend the worldline description of vector and antisymmetric tensor fields coupled to gravity to the massive case. In particular, we derive a worldline path integral representation for the one-loop effective action of a massive antisymmetric tensor field of rank p (a massive p-form) whose dynamics is dictated by a standard Proca-like lagrangian coupled to a background metric. This effective action can be computed in a proper time expansion to obtain the corresponding Seeley-DeWitt coefficients a0, a1, a2. The worldline approach immediately shows that these coefficients are derived from the massless ones by the simple shift D -> D+1, where D is the spacetime dimension. Also, the worldline representation makes it simple to derive exact duality relations. Finally, we use such a representation to calculate the one-loop contribution to the graviton self-energy due to both massless and massive antisymmetric tensor fields of arbitrary rank, generalizing results already known for the massless spin 1 field (the photon).

On the dimensional dependence of duality groups for massive p-forms

We study the soldering formalism in the context of Abelian p-form theories. We develop further the fusion process of massless antisymmetric tensors of different ranks into a massive p-form and establish its duality properties. To illustrate the formalism we consider two situations. First the soldering mass generation mechanism is compared with the Higgs and Julia–Toulouse mechanisms for mass generation due to condensation of electric and magnetic topological defects. We show that the soldering mechanism interpolates between them for even-dimensional spacetimes, in this way confirming the Higgs/Julia–Toulouse duality proposed by Quevedo and Trugenberger [Nucl. Phys. B 501 (1997) 143] a few years ago. Next, soldering is applied to the study of duality group classification of the massive forms. We show a dichotomy controlled by the parity of the operator defining the symplectic structure of the theory and find their explicit actions.

Propagator for a general form field inAdSd+1space

Using the known propagator equations for 0,1 and 2 forms in AdS_{d+1}, we find the p-form field propagator equations in dimensions where the forms are Poincare dual. Since the general equation obeyed by the propagators is linear in dimension, this gives us the equation obeyed by the propagators for any d. Furthermore, based on the Poincare duality formulas for 0,1,2 and 3 forms we conjecture the general form of the Poincare duality formulas, and check them against the previously found propagator equations. The whole structure is self-consistent. Once we have the equations, we can easily obtain all the p-form field propagators in AdS_{d+1}. The generalization to massive p-forms can also be easily done.

Propagators for massive symmetric tensor and p-forms in AdSd+1

We construct propagators in Euclidean AdS(d+1) space-time for massive p-forms and massive symmetric tensors.

Correlators of currents corresponding to the massive p-form fields in AdS/ CFT correspondence

By solving the equations of motion of massive p-form potential in Anti-de-Sitter space and using the AdS/ CFT correspondence of Maldacena, the generating functional of two-point correlation functions of the currents is obtained. When the mass parameter vanishes the result agrees with the known massless case.