Sumit R. Das

Comparing decay rates for black holes and D-branes

We compute the leading order (in coupling) rate of emission of low energy quanta from a slightly non-extremal system of 1-D- and 5-D-branes. We also compute the classical cross-section, and hence the Hawking emission rate, for low energy scalar quanta for the black hole geometry that corresponds to these branes (at sufficiently strong coupling). These rates are found to agree with each other.

STRING FIELD THEORY AND PHYSICAL INTERPRETATION OF D=1 STRINGS

We describe a field theoretic formulation for one-dimensional string theory. It is given by the collective field representation of the matrix model and leads to a physical interpretation of the theory as that of a massless scalar field in two dimensions. The additional dimension, coming from the large-N color of the matrix model, has an extent which goes to infinity in the continuum limit. The interactions of the field theory are non-zero only at the boundaries of this additional dimension.

Vibration modes of giant gravitons

We examine the spectrum of small vibrations of giant gravitons when the gravitons expand in antichar21{}de Sitter space and when they expand on the sphere. For any given angular harmonic, the modes are found to have frequencies related to the curvature length scale of the background; these frequencies are independent of radius (and hence angular momentum) of the brane itself. This implies that the holographic dual theory must have, in a given R charge sector, low-lying non-BPS excitations with level spacings independent of the R charge.

Excitations of D strings, entropy and duality

We examine the BPS and low energy non-BPS excitations of the D-string in terms of open strings that travel on the D-string. We use this to study the energy thresholds for exciting a long D-string, for arbitrary winding number. We also compute the leading correction to the entropy from non-BPS states for a long D-string, and observe the relation of all these quantities with the corresponding quantities for the elementary string.

INTERACTIONS INVOLVING D-BRANES

Abstract We investigate some aspects of the spectrum of D-branes and their interactions with closed strings. As argued earlier, a collection of many D-strings behaves at large dilaton values as a single multiply wound string. We use this result and T -duality transformations to show that a similar phenomenon occurs for effective strings produced by wrapping p -branes on a small ( p − 1)-dimensional torus, for suitable coupling. To understand the decay of an excited D-string at large dilaton values, we study the decay of an elementary string at small dilaton values. A long string, multiply wound on a circle, with a small excitation energy is found to predominantly decay into another string with the same winding number, and an unwound closed string (rather than two wound strings). This decay amplitude agrees, under duality, with the decay amplitude computed using the Born-Infeld action for the D-string. We compute the absorption cross section for the D-brane model studied by Callan and Maldacena. The absorption cross section for the dilaton equals that for the scalars obtained by reduction of the graviton, and both agree with the cross section expected from a classical hole with the same charges.

Giant gravitons, Bogomol'nyi-Prasad-Sommerfield bounds, and noncommutativity

It has been recently suggested that gravitons moving in AdS m × S n spacetimes along the S n blow up into spherical (n−2) branes whose radius increases with increasing angular momentum. This leads to an upper bound on the angular momentum, thus explaining the stringy exclusion principle. We show that this bound is present only for states which saturate a BPS-like condition involving the energy E and angular momentum J, E ≥ J/R, where R is the radius of S n. Restriction of motion to such states lead to a noncommuta-tivity of the coordinates on S n. As an example of motions which do not obey the exclusion principle bound, we show that there are finite action instanton configurations interpolating between two possible BPS states. We suggest that this is consistent with the proposal that there is an effective description in terms of supergravity defined on noncommutative spaces and noncommutativity arises here because of imposing supersymmetry.

Magnetic Moments of Branes and Giant Gravitons

We study the magnetic analogue of Myers Dielectric Effect and, in some cases, relate it to the blowing up of particles into branes, first investigated by Greevy, Susskind and Toumbas. We show that D0-branes or gravitons in M-theory, moving in a magnetic four-form field strength background expand into a non-commutative two sphere. Both examples of constant magnetic field and non-constant fields in curved backgrounds generated by branes are considered. We find, in all cases, another solution, consisting of a two-brane wrapping a classical two-sphere, which has all the quantum numbers of the D0-branes. Motivated by this, we investigate the blowing up of gravitons into branes in backgrounds different from AdSm × Sn. We find the phenomenon is quite general. In many cases with less or even no supersymmetry we find a brane configuration which has the same quantum numbers and the same energy as a massless particle in supergravity.

Derivative corrections from noncommutativity

We show that an infinite subset of the higher-derivative α corrections to the DBI and Chern-Simons actions of ordinary commutative open-string theory can be determined using noncommutativity. Our predictions are compared to some lowest order α corrections that have been computed explicitly by Wyllard (hepth0008125), and shown to agree.

Supergravity with self-dual B fields and Instantons in noncommutative gauge theory

We study type-IIB supergravity in the presence of (euclidean) D3 branes and nonzero self-dual B-fields. We point out that the Einstein frame metric is identical to the full geometry for D3 branes without B fields turned on. Furthermore, in a decoupling limit in which the theory is conjectured to be dual to noncommutative Yang-Mills theory, the entire Einstein metric remains intact, and in particular, is asymptotically flat. We construct D-instanton solutions in this geometry. We show that in the decoupling limit the D-instanton action agrees with the action of the corresponding instanton in the noncommutative Yang-Mills theory and is expressed in terms of the open string coupling. Some other aspects of this correspondence, which have unusual features because the underlying metric is asymptotically flat, are explored.

Folds, bosonization and non-triviality of the classical limit of 2D string theory

Abstract In the 1-dimensional matrix model one identifies the tachyon field in the asymptotic region with a nonlocal transfom of the density of fermions. But there is a problem in relating the classical tachyon field with the surface profile of the Fermi fluid if a fold forms in the Fermi surface. Besides the collective field additional variables w j ( x ) are required to desrcibe folds. In the quantum theory we show that the w j are the quantum dispersions of the collective field. These dispersions become O (1) rather than O( l ) precisely after fold formation, thus giving additional “classical” quantities and leading to a rather nontrivial classical limit. A coherent pulse reflecting from the potential wall turns into high energy incoherent quanta (if a fold forms), the frequency amplification being of the order of the square root of the number of quanta in the incident wave.