Room 326

Self-dual forms: Action and Hamiltonian

Varun Gupta

IMSc

Writing down an action formalism for the theories with the
chiral 2n-form fields(with self-dual field strengths) in the general 4n+2
dimensions has been a challenge for many years. While various
models/formalisms exist in the literature, each of them also have their
shortcomings.

For example, the formalism developed by Pasti, Sorokin and Tonin('96) gives
a good action by introducing an auxiliary scalar field. However, the
additional terms due to the new field are not polynomial. It has
derivatives of a scalar field present in its denominator making the
Lagrangian singular when the scalar field is constant in spacetime.

In his work 1511.08220, Sen has 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 the
paper 1903.12196, he analyzes the canonical formulation of these theories
and shows 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.

In the talk. From the paper 1903.12196, I will take the case n=1(of 6d
theories) with 3-form field strength and discuss the splitting in the
Hamiltonian after doing a suitable gauge fixing procedure.