Self-dual forms: Action, Hamiltonian and Compactification (1903.12196v2)

Abstract: It has been shown that, by adding an extra free field that decouples from the dynamics, one can construct actions for interacting 2n-form fields with self-dual field strengths in 4n+2 dimensions. In this paper we analyze canonical formulation of these theories, and show that the resulting Hamiltonian reduces to the sum of two Hamiltonians with independent degrees of freedom. One of them is free and has no physical consequence, while the other contains the physical degrees of freedom with the desired interactions. For the special cases of chiral scalars in two dimensions and chiral two form fields in six dimensions, we discuss compactification of these theories respectively on a circle and a two dimensional torus, and show that we recover the expected properties of these systems, including S-duality invariance in four dimensions.

• The paper proposes a novel framework by introducing an auxiliary free field which enables the consistent formulation of self-dual fields' canonical actions and dynamics.
• The Hamiltonian formulation distinctly separates physical interacting fields from decoupled free fields, ensuring proper Dirac bracket commutation and preserving Lorentz invariance.
• The study demonstrates that under compactification, self-dual fields retain S-duality invariance, paving the way for deeper insights in type IIB string theory and higher-dimensional supergravity.

An Analysis of Self-Dual Forms: Action, Hamiltonian, and Compactification

This paper, authored by Ashoke Sen, delivers a detailed exposition on the canonical formulation of theories involving self-dual fields in dimensions 4n+2, best exemplified through the lens of string theory. The paper proposes a framework that circumvents several pre-existing challenges associated with devising actions for these systems. Specifically, it presents a methodology incorporating an additional free field, which, while decoupling from dynamics, allows for the contrivance of novel actions for interacting 2n-form fields exhibiting self-dual field strengths.

Canonical Formulation and Hamiltonian Analysis

A critical contribution of this paper lies within the canonical formulation of the proposed action. The Hamiltonian, as articulated, distinctively bifurcates into a pair of Hamiltonians representing decoupled systems: one associated with free fields, deemed physically inconsequential, and another embracing interacting fields with the intended dynamics. Notably, the descriptions maintain S-duality invariance under compactification, hence preserving essential systemic symmetry, especially within four-dimensional constructs. This separation is diligently demonstrated through the Dirac brackets ensuring the mutual commutation of physical and free degrees of freedom in quantum theory.

Compactification and Dimensional Reduction

Further exploration is accorded to specific cases – particularly, chiral scalars in two dimensions compactified on a circle and chiral two-form fields in six-dimensional settings reduced on a torus. The paper of these special instances underscores the paper's underlying framework, revealing expected dynamics such as duality invariances, and the adept handling of metric coupling within unconventional boundaries. Particularly in six-dimensional analyses, the work embraces the reformulation of the involved action to facilitate studies on dimensional reduction, casting light on the invariant properties pertinent to S-duality transformations.

Implications and Future Perspectives

The implications of this research are profound within both theoretical and practical realms. By adeptly handling self-dual systems without compromising Lorentz invariance or engaging infinite auxiliary fields, potential pathways open for broader application within the domain of type IIB string theory scenarios and supergravity models. The results contribute pivotal insights toward understanding duality and compactification phenomena in higher-dimensional theories, serving as a springboard for future exploratory pursuits in theoretical physics and quantum field theory landscapes.

Continued research along this trajectory promises to unravel deeper correlations across dimensional settings while promoting enhanced understanding of duality and symmetry across multifaceted field theories. The methodologies outlined could inspire advancements in both the mathematical structures of theoretical models and their empirical applications across a spectrum of physics undertakings.