Double dimensional reduction of M5-brane action in Sen formalism

Abstract

In this paper, we present double dimensional reduction of the complete M5-brane action in the Sen formalism of self-dual form. Although in this formalism the gravity couples to the independent pseudo-$2$-form and pseudo-$3$-form fields in a non-standard and very complicated way, the double dimensional reduction on the complete action can be carried out. This is by dualising some components of the pseudo-$2$-form field and integrating out the pseudo-$3$-form field. We show explicitly that the double dimensional reduction on a circle gives rise to the complete D4-brane or the complete dual D4-brane action depending on what components of the pseudo-$2$-form field are dualised. The duality between the D4-brane and dual D4-brane actions are realised in the viewpoint of the Sen formalism as the swapping of the roles of the components of the pseudo-$2$-form field between those which are dualised and those which remain. We also make a brief outline on how to generalise this to the cases of dimensional reduction on some other spaces as well as how to understand the duality of reduced action from the viewpoint of the Sen formalism. An explicit example for dimensional reduction of the quadratic six-dimensional action on a torus is given and the realisation of its S-duality is also discussed.

arXiv comment20 pages, no figure; slight edit of texts; Version submitted and accepted by EPJ C

References in corpus (23)

• Covariant Action for the Super-Five-Brane of M-Theory
• Covariant Action for a D=11 Five-Brane with the Chiral Field
• World-Volume Action of the M Theory Five-Brane
• Interacting Chiral Gauge Fields in Six Dimensions and Born-Infeld Theory
• Dual D-Brane Actions
• Coupling a Self-Dual Tensor to Gravity in Six Dimensions
• Covariant Action for Type IIB Supergravity
• Self-dual forms: Action, Hamiltonian and Compactification
• On Covariant Actions for Chiral $p-$Forms
• (2,0) Lagrangian Structures
• Duality of Self-Dual Actions
• Three approaches to chiral form interactions
• M5 on a torus and the three brane
• Lagrangian Formulations of Self-dual Gauge Theories in Diverse Dimensions
• The M5-brane action revisited
• Geometrical Aspects of An Abelian (2,0) Action
• Covariant M5-brane action with self-dual 3-form
• Duality and Fluxes in the Sen Formulation of Self-Dual Fields
• Lagrangian of Self-dual Gauge Fields in Various Formulations
• A nonabelian M5 brane Lagrangian in a supergravity background
• Null Reductions of M5-Branes
• The Dual Formulation of M5-brane Action
• A covariantisation of M5-brane action in dual formulation

Cited by in corpus (4)

• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• Manifestly Covariant Polynomial M5-brane Lagrangians
• Monopoles, Clarified
• Nonlinear chiral forms in the Sen formulation