We compute the one-loop effective action of the Horava theory, in its
nonprojectable formulation. The quantization is performed in the
Batalin-Fradkin-Vilkovisky formalism. It includes the second-class constraints
and the appropriate gauge-fixing condition. The ghost fields associated with
the second-class constraints can be used to get the integrated form of the
effective action, which has the form of a Berezinian. We show that all
irregular loops cancel between them in the effective action. The key for the
cancellation is the role of the ghosts associated with the second-class
constraints. These ghosts form irregular loops that enter in the denominator of
the Berezinian, eliminating the irregular loops of the bosonic nonghost sector.
Irregular loops produce dangerous divergences; hence their cancellation is an
essential step for the consistency of the theory. The cancellation of this kind
of divergences is in agreement with the previous analysis done on the quantum
canonical Lagrangian and its Feynman diagrams.
The conclusions of the text are as follows:
- The one-loop effective action of the Horava theory, in its nonprojectable formulation, has been computed.
- The quantization of the theory was performed using the Batalin-Fradkin-Vilkovisky formalism.
- It includes the second-class constraints and the appropriate gauge-fixing condition.
- The ghost fields associated with the second-class constraints were used to obtain the integrated form of the effective action, which takes the form of a Berezinian.
- All irregular loops cancel between them in the effective action, and this cancellation is crucial for the consistency of the theory.
- The cancellation of these irregular loops is in line with previous analyses done on the quantum canonical Lagrangian and its Feynman diagrams.
Future Roadmap
Potential Challenges
- Further understanding and analysis of the Horava theory and its nonprojectable formulation may be required to address potential challenges.
- Exploring higher-loop effective actions and their cancellations to ensure the consistency of the theory.
Potential Opportunities
- Building upon the results of this study, researchers can investigate the implications of the cancellations in the one-loop effective action for the overall behavior of the Horava theory.
- Exploring the connection between the cancellation of irregular loops and the quantum canonical Lagrangian can provide deeper insights into the underlying principles of the theory.
- These findings may open up avenues for further research and development in quantum field theories and their applications.
Note: The conclusions and roadmap provided here are based on the given text. Additional context and information may be required for a more comprehensive analysis.