Abstract
We construct new type of non-relativistic D-branes which are defined with the help of T-duality along null direction. We find Lagrangian and Hamiltonian formulation of these D-branes and study their properties under T-duality transformations.
Highlights
As the step in our analysis we will study properties of this non-relativistic D(p-1)brane when it wraps another compact direction
We construct new type of non-relativistic D-branes which are defined with the help of T-duality along null direction
We show an alternative way how to define Hamiltonian for non-relativistic D(p-1)brane in torsional NC geometry which is based on the canonical description of T-duality
Summary
We formulate non-relativistic D-brane in the Lagrangian formalism. The starting point is an action for Dp-brane in general background that has the form. Our goal is to define non-relativistic D(p-1)-brane as T-dual of relativistic Dp-brane in the background with null isometry This approach is based on seminal paper [8] where an action for non-relativistic string was proposed. It was shown in [10] that such a string corresponds to the string that is T-dual to the string in the null background. The action (2.9) is our proposal for non-relativistic D(p-1)-brane It is invariant under world-volume diffeomorphism and it is manifestly covariant. It is instructive to give an explicit example of D1-brane In this case the matrix inverse Aαˆβhas following form 1 det Aαˆβ. We see that the expression under square root has similar structure as non-relativistic string action that was found in [8] which is nice consistency check of our proposal
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