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Area of Science:

  • Theoretical Physics
  • Mathematical Physics
  • High Energy Physics

Background:

  • Understanding field theories and their consistency conditions is crucial in theoretical physics.
  • Existing models often rely on action principles or off-shell conservation for consistency.

Purpose of the Study:

  • To construct a novel class of interacting (d-2)-form theories in d dimensions.
  • To explore theories with a
  • third-way
  • consistency, where interaction terms are neither purely from action variations nor off-shell conserved.
  • To investigate generalizations and extensions of these theories.

Main Methods:

  • Developing a new construction method for interacting p-form theories.
  • Analyzing the consistency conditions of the field equations of motion.
  • Exploring couplings to other forms and higher derivative extensions.

Main Results:

  • Successfully constructed a class of interacting (d-2)-form theories exhibiting
  • third-way
  • consistency.
  • Demonstrated that these theories remain on-shell consistent despite non-standard interaction terms.
  • Showcased generalizations, including couplings to (d-3)-forms and the prominent role of three-algebras.
  • Recovered modified three-dimensional Yang-Mills theory and enabled higher derivative extensions.

Conclusions:

  • The proposed construction method offers a flexible approach to building consistent field theories.
  • The concept of
  • third-way
  • consistency expands the landscape of theoretical models.
  • This framework provides a pathway for developing more complex and extended theoretical models in physics.