Branes \\\\ A Note

Branes A Note Johar M. Ashfaque The ends of open strings couple to D-branes. In fact, the open string spectrum carries the fluctuations of the D-branes. Therefore in superstring theory D-branes receive fermionic degrees of freedom. The spectrum of open strings coupled to a Dp-brane is given by • The massless modes are described by N = 1 super Yang-Mills theory reduced to (p + 1) dimensions a theory that has a vector field, 16 fermionic spinor fields and 9 − p scalar degrees of freedom • The spectrum has a tower of heavy string modes • A scalar tachyon may be present

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Stable Dp-Branes

Some Dp-branes are stable while others are not. The presence of an open string tachyon indicates instability of the D-brane. • D-branes in bosonic string theory are always unstable • Dp-branes for II-A superstring are stable for p even • Dp-branes for II-B superstring are stable for p odd Stability is related to supersymmetry. The boundary conditions break some of the symmetry.

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Supergravity p-Branes

D-branes are non-perturbative objects, they are not seen perturbatively due to their large mass. Stable Dp-branes have a low-energy limit as solutions to the supergravity equations of motions the so-called p-branes. The p-branes are supported by a (p + 1)-form, gravity and the dilation field. The stable p-branes enjoy several useful features: • A p-brane carries (p + 1)-form charge. The charge prevents the p-branes from evaporating. • The charge density is proportional to the mass density. • 16/32 supersymmetries are preserved: the so-called 1/2 BPS condition where half the supersymmetry is conserved. • There is a non-renormalization theorem for 1/2 BPS objects: p-branes are independent of the coupling strength. Hence 1/2 BPS p-branes describe Dp-branes exactly.

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