# Self-dual forms: Action, Hamiltonian and Compactification

## TL;DR

This paper analyzes the canonical formulation of self-dual form theories in specific dimensions, revealing a Hamiltonian structure with decoupled free and interacting parts, and explores their compactifications and dualities.

## Contribution

It provides a detailed canonical analysis of self-dual form actions, showing the Hamiltonian decomposes into independent parts and examining their properties under compactification.

## Key findings

- Hamiltonian reduces to sum of two independent Hamiltonians.
- One Hamiltonian describes free, decoupled degrees of freedom.
- Compactification recovers expected duality properties.

## 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.