3D Supergravity in the Batalin-Vilkovisky Formalism

Area of Science:

• Theoretical Physics
• Mathematical Physics

Background:

• The Batalin-Vilkovisky (BV) formalism provides a powerful framework for quantizing gauge theories.
• Three-dimensional supergravity theories present unique challenges and opportunities for theoretical investigation.

Purpose of the Study:

• To construct a three-dimensional supergravity theory within the Batalin-Vilkovisky formalism.
• To demonstrate the equivalence between this constructed theory and an AKSZ (Alexandrov-Kononov-Schwarz-Veselov) theory.

Main Methods:

• Utilizing the Batalin-Vilkovisky formalism for the construction of the supergravity theory.
• Incorporating the Rarita-Schwinger term into the theory.
• Establishing the equivalence to an AKSZ theory through rigorous mathematical methods.

Main Results:

• A consistent construction of three-dimensional supergravity in the Batalin-Vilkovisky formalism has been achieved.
• The inclusion of the Rarita-Schwinger term is shown to be crucial for this construction.
• The formulated theory is demonstrated to be equivalent to a known AKSZ theory.

Conclusions:

• The Batalin-Vilkovisky formalism is a suitable framework for constructing three-dimensional supergravity.
• The equivalence to AKSZ theories provides a deeper understanding of the underlying structure of supergravity.
• This work opens avenues for further exploration of higher-dimensional supergravities and related topological field theories.