arXiv subjects

Mark Van Raamsdonk

Publications and source records attributed to Mark Van Raamsdonk.

98 records · Page 6Linked to original sources

arXiv1999

Noncommutative Perturbative Dynamics

We study the perturbative dynamics of noncommutative field theories on R^d, and find an intriguing mixing of the UV and the IR. High energies of virtual particles in loops produce non-analyticity at low momentum. Consequently, the low energy effective action is singular at zero momentum even when the original noncommutative field theory is massive. Some of the nonplanar diagrams of these theories are divergent, but we interpret these divergences as IR divergences and deal with them accordingly. We explain how this UV/IR mixing arises from the underlying noncommutativity. This phenomenon is reminiscent of the channel duality of the double twist diagram in open string theory.

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arXiv1999

Multiple Dp-branes in Weak Background Fields

We find the terms in the nonabelian world-volume action of a system of many Dp-branes which describe the leading coupling to all type II supergravity background fields. These results are found by T-dualizing earlier results for D0-branes, which in turn were determined from calculations of the M(atrix) theory description of the supercurrent of 11D supergravity. Our results are compatible with earlier results on the supersymmetric Born-Infeld action for a single D-brane in a general background and with Tseytlin's symmetrized trace proposal for extending the abelian Born-Infeld action to a nonabelian theory. In the case p = 3, the operators we find on the D-brane world-volume are closely related to those which couple to supergravity fields in the AdS_5 * S^5 IIB supergravity background. This gives an explicit construction, including normalization, of some of the operators used in the celebrated AdS/CFT correspondence for 3-branes. We also discuss the S-duality of the action in the case p = 3, finding that the S-duality of the action determines how certain operators in the 4D N = 4 SYM theory transform under S-duality. These S-duality results give some new insight into the puzzle of the transverse 5-brane in M(atrix) theory.

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arXiv1999

Absorption of dilaton partial waves by D3-branes

We calculate the leading term in the low-energy absorption cross section for an arbitrary partial wave of the dilaton field by a stack of many coincident D3-branes. We find that it precisely reproduces the semiclassical absorption cross section of a 3-brane geometry, including all numerical factors. The crucial ingredient in making the correspondence is the identification of the precise operators on the D3-brane world-volume which couple to the dilaton field and all its derivatives. The needed operators are related through T-duality and the IIA/M-theory correspondence to the recently determined M(atrix) theory expressions for multipole moments of the 11D supercurrent. These operators have a characteristic symmetrized trace structure which plays a key combinatorial role in the analysis for the higher partial waves. The results presented here give new evidence for an infinite family of non-renormalization theorems which are believed to exist for two-point functions in ${\cal N} = 4$ gauge theory in four dimensions.

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arXiv1999

Multiple D0-branes in Weakly Curved Backgrounds

We investigate further our recent proposal for the form of the matrix theory action in weak background fields. Using Seiberg's scaling argument we relate the matrix theory action to a low-energy system of many D0-branes in an arbitrary but weak NS-NS and R-R background. The resulting multiple D0-brane action agrees with the known Born-Infeld action in the case of a single brane and gives an explicit formulation of many additional terms which appear in the multiple brane action. The linear coupling to an arbitrary background metric satisfies the nontrivial consistency condition suggested by Douglas that the masses of off-diagonal fields are given by the geodesic distance between the corresponding pair of D0-branes. This agreement arises from combinatorial factors which depend upon the symmetrized trace ordering prescription found earlier for higher moments of the matrix theory stress-energy tensor. We study the effect of a weak background metric on two graviton interactions and find that our formalism agrees with the results expected from supergravity. The results presented here can be T-dualized to give explicit formulae for the operators in any D-brane world-volume theory which couple linearly to bulk gravitational fields and their derivatives.

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arXiv1999

Supergravity currents and linearized interactions for Matrix Theory configurations with fermionic backgrounds

The leading terms in the long-range interaction potential between an arbitrary pair of matrix theory objects are calculated at one-loop order. This result generalizes previous calculations by including arbitrary fermionic background field configurations. The interaction potential at orders 1/r^7 and 1/r^8 is shown to correspond precisely with the leading terms expected from linearized supergravity interactions between arbitrary objects in M-theory. General expressions for the stress tensor, membrane current and 5-brane current of an arbitrary matrix configuration are derived, including fermionic contributions. Supergravity effects which are correctly reproduced include membrane/5-brane interactions, 0-brane/6-brane interactions, supercurrent/supercurrent interactions and the spin contributions to moments of the supergravity currents. The matrix theory description of the supergravity stress tensor, membrane current and 5-brane current are used to propose an explicit formulation of matrix theory in an arbitrary background metric and 3-form field.

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arXiv1998

Three-graviton scattering in Matrix theory revisited

We consider a subset of the terms in the effective potential describing three-graviton interactions in Matrix theory and in classical eleven-dimensional supergravity. In agreement with the results of Dine and Rajaraman, we find that these terms vanish in Matrix theory. We show that the absence of these terms is compatible with the classical supergravity theory when the theory is compactified in a lightlike direction, resolving an apparent discrepancy between the two theories. A brief discussion is given of how this calculation might be generalized to compare the Matrix theory and supergravity descriptions of an arbitrary 3-body system.

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arXiv1998

Conservation of Supergravity Currents from Matrix Theory

In recent work by Kabat and Taylor, certain Matrix theory quantities have been identified with the spatial moments of the supergravity stress-energy tensor, membrane current, and fivebrane current. In this note, we determine the relations between these moments required by current conservation, and prove that these relations hold as exact Matrix Theory identities at finite N. This establishes conservation of the effective supergravity currents (averaged over the compact circle). In addition, the constraints of current conservation allow us to deduce Matrix theory quantities corresponding to moments of the spatial current of the longitudinal fivebrane charge, not previously identified.

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arXiv1998

Angular momentum and long-range gravitational interactions in Matrix theory

We consider subleading terms in the one-loop Matrix theory potential between a classical membrane state and a supergraviton. Nontrivial terms arise at order v/r^8 and v^3/r^8 which are proportional to the angular momentum of the membrane state. The effective potential for a graviton moving in a boosted Kerr-type metric is computed and shown to agree precisely with the Matrix theory calculation at leading order in the long-distance expansion for each power of the graviton velocity. This result generalizes to arbitrary order; we show that terms in the membrane-graviton potential corresponding to nth moments of the membrane stress-energy tensor are reproduced correctly to all orders in the long-distance expansion by terms of the form F^4 X^n in the one-loop Matrix theory calculation.

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