A Matrix Model for Static Configurations of M-Theory

Nuclear Physics B, 1998

We present a study of M(atrix) theory from a purely canonical viewpoint. In particular, we identify free particle asymptotic states of the model corresponding to the supergraviton multiplet of eleven dimensional supergravity. These states have a natural interpretation as excitations in the flat directions of the matrix model potential. Furthermore, we provide the split of the matrix model Hamiltonian into a free part describing the free propagation of these particle states along with the interaction Hamiltonian describing their interactions. Elementary quantum mechanical perturbation theory then yields an effective potential for these particles as an expansion in their inverse separation. Remarkably we find that the leading velocity independent terms of the effective potential cancel in agreement with the fact that there is no force between stationary D0 branes. The scheme we present provides a framework in which one can perturbatively compute the M(atrix) theory result for the eleven dimensional supergraviton S matrix.

2001

Physics Letters B, 1996

We present a class of black p-brane solutions of M-theory which were hitherto known only in the extremal supersymmetric limit, and calculate their macroscopic entropy and temperature.

The issue of justifying the matrix-theory proposal is revisited. We first discuss how the matrix-string theory is derived directly starting from the eleven dimensional supermem- brane wrapped around a circle of radius R = gsℓs, without invoking any stringy assump- tions, such as S- and T-dualities. This derivation provides us a basis for studying both string (R → 0)- and M (R → ∞)-theory limits of quantum membrane theory in a single unified framework. In particular, we show that two different boosts of supermembrane, namely one of unwrapped membrane along the M-theory circle and the other of membrane wrapped about a transervse direction which is orthogonal to the M-theory circle, give the same matrix theory in the 11 dimensional limit, R → ∞ (with N → ∞). We also discuss briefly the nature of possible covariantized matrix (string) theories.

2000

Physics Letters B, 1998

We discuss, in the context of M(atrix) theory, the creation of a membrane suspendend between two longitudinal five-branes when they cross each other. It is shown that the membrane creation is closely related to the degrees of freedom in the off-diagonal blocks which are related via dualities to the chiral fermionic zero mode on a 0-8 string. In the dual system of a D0-brane and a D8-brane in type II A theory the half-integral charges associated with the "half"-strings are found to be connected to the well-known fermion-number fractionalization in the presence of a fermionic zero mode. At sufficiently short distances, the effective potential between the two five-branes is dominated by the zero mode contribution to the vacuum energy.

Journal of High Energy Physics, 2000

In this paper, the low-energy effective dynamics of M-theory, eleven-dimensional supergravity, is taken off-shell in a manifestly supersymmetric formulation. We show that a previously proposed relaxation of the superspace torsion constraints does indeed accommodate a current supermultiplet which lifts the equations of motion corresponding to the ordinary second order derivative supergravity lagrangian. Whether the auxiliary fields obtained this way can be used to construct an off-shell lagrangian is not yet known. We comment on the relation and application of this completely general formalism to higher-derivative (R^4) corrections. Some details of the calculation are saved for a later publication.

Nuclear Physics B, 2006

We classify the supersymmetric mass deformations of all the super Yang-Mills quantum mechanics, which are obtained by dimensional reductions of minimal super Yang-Mills in spacetime dimensions: ten, six, four, three and two. The resulting actions can be viewed as the matrix descriptions of supermembranes in nontrivial backgrounds of one higher dimensional supergravity theories. We also discuss the utmost generalization of the light-cone formulation of the Nambu-Goto action for a p-brane, including time dependent backgrounds.

Nuclear Physics B, 1996

We discuss the relation between M theory and type II string theories. We show that, assuming "natural" interactions between membranes and fivebranes in M theory, the known interactions between strings and D-branes in type II string theories arise in appropriate limits. Our discussion of the interactions is purely at the classical level. We remark on issues associated with the M theory approach to enhanced gauge symmetries, which deserve further investigation.

Nuclear Physics B, 2005

We proceed further with a study of open supermembrane on the AdS 4/7 ×S 7/4 backgrounds. Open supermembrane can have M5-brane and 9-brane as Dirichlet branes. In AdS and pp-wave cases the configurations of Dirichlet branes are restricted. A classification of possible Dirichlet branes, which is given up to and including the fourth order of fermionic variable θ in hepth/0310035, is shown to be valid even at full order of θ. We also discuss open M5-brane on the AdS 4/7 × S 7/4 .

Nuclear Physics B, 2001

Five-branes lead in four dimensions to massless N = 1 supermultiplets if M-theory is compactified on S 1 /Z 2 × (a Calabi-Yau threefold). One of them describes the modulus associated with the position of the five-brane along the circle S 1 . We derive the effective four-dimensional supergravity of this multiplet and its coupling to bulk moduli and to Yang-Mills and charged matter multiplets located on Z 2 fixed planes. The dynamics of the five-brane modes is obtained by reduction and supersymmetrization of the covariant five-brane bosonic action. Our construction respects all symmetries of M-theory, including the self-duality of the brane antisymmetric tensor. Corrections to gauge couplings are strongly constrained by this selfduality property. The brane contribution to the effective scalar potential is formally similar to a renormalization of the dilaton. The vacuum structure is not modified. Altogether, the impact of the five-brane modulus on the effective supergravity is reminiscent of string one-loop corrections produced by standard compactification moduli.

AIP Conference Proceedings

After reviewing how M-theory subsumes string theory, we report on some new and interesting developments, focusing on the "brane-world": circumventing no-go theorems for supersymmetric brane-worlds and complementarity of the Maldacena and Randall-Sundrum pictures. We also discuss the quantum M-» 0 discontinuity of massive gravity with a A term. My talk is in three parts. In section 1 we briefly review M-theory, in section 2 we discuss some recent developments on the brane-world and finally in section 3 we address the issue of whether the graviton can have a mass.

1987

We discuss the relation between M theory and type II string theories. We show that, assuming “natural ” interactions between membranes and fivebranes in M theory, the known interactions between strings and D-branes in type II string theories arise in appropriate limits. Our discussion of the interactions is purely at the classical level. We remark on issues associated with the M theory approach to enhanced gauge symmetries, which deserve further investigation.

Journal of High Energy Physics, 2018

We analyze the four-point function of stress-tensor multiplets for the 6d quantum field theory with OSp(8 * |4) symmetry which is conjectured to be dual to M-theory on AdS 7 × S 4 , and deduce the leading correction to the tree-level supergravity prediction by obtaining a solution of the crossing equations in the large-N limit with the superconformal partial wave expansion truncated to operators with zero spin. This correction corresponds to the M-theoretic analogue of R 4 corrections in string theory. We also find solutions corresponding to higher-spin truncations, but they are subleading compared to the 1-loop supergravity prediction, which has yet to be calculated.

Arxiv preprint hep-th/0410100, 2004

Close studies of the solitonic solutions of D=11 N=1 supergravity theory provide a deeper understanding of the elusive M-theory and constitute steps towards its final formulation. In this work, we propose the use of calibration techniques to find localized intersecting brane solutions of the theory. We test this hypothesis by considering Kahler and special Lagrangian calibrations. We also discuss the interpretation of some of these results as branes wrapped or reduced over supersymmetric cycles of Calabi-Yau manifolds and we find the corresponding solutions in D=5 N=2 supergravity.