#### 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.

Done