Martin Kruczenski

Spiky strings and giant magnons on S5

Recently, classical solutions for strings moving in AdS5 × S5 have played an important role in understanding the AdS/CFT correspondence. A large set of them were shown to follow from an ansatz that reduces the solution of the string equations of motion to the study of a well-known integrable 1-d system known as the Neumann-Rosochatius (NR) system. However, other simple solutions such as spiky strings or giant magnons in S5 were not included in the NR ansatz. We show that, when considered in the conformal gauge, these solutions can be also accomodated by a version of the NR-system. This allows us to describe in detail a giant magnon solution with two additional angular momenta and show that it can be interpreted as a superposition of two magnons moving with the same speed. In addition, we consider the spin chain side and describe the corresponding state as that of two bound states in the infinite SU(3) spin chain. We construct the Bethe ansatz wave function for such bound state.

Spherically collapsing matter in AdS, holography, and shellons

Abstract We investigate the collapse of a spherical shell of matter in an anti-de Sitter space. We search for a holographic description of the collapsing shell in the boundary theory. It turns out that in the boundary theory it is possible to find information about the radial size of the shell. The shell deforms the background spacetime, and the deformed background metric enters into the action of a generic bulk field. As a consequence, the correlators of operators coupling to the bulk field are modified. By studying the analytic structure of the correlators, we find that in the boundary theory there are unstable excitations (“shellons”) whose masses are multiples of a scale set by the radius of the shell. We also comment on the relation between black hole formation in the bulk and thermalization in the boundary.

Vacua, propagators, and holographic probes in AdS/CFT

In this paper we investigate the relation between the bulk and boundary in AdS/CFT. We first discuss the relation between the Poincare and the global vacua, and then study various probes of the bulk from the boundary theory point of view. We derive expressions for retarded propagators and note that objects in free fall look like expanding bubbles in the boundary theory. We also study several Yang-Mills theory examples where we investigate thermal screening and confinement using propagators. In the case of confinement we also calculate the profile of a flux tube and provide an alternative derivation of the tension.

Black hole formation in AdS and thermalization on the boundary

We investigate black hole formation by a spherically collapsing thin shell of matter in AdS space. This process has been suggested to have a holographic interpretation as thermalization of the CFT on the boundary of the AdS space. The AdS/CFT duality relates the shell in the bulk to an off-equilibrium state of the boundary theory which evolves towards a thermal equilibrium when the shell collapses to a black hole. We use 2-point functions to obtain information about the spectrum of excitations in the off-equilibrium state, and discuss how it characterizes the approach towards thermal equilibrium. The full holographic interpretation of the gravitational collapse would require a kinetic theory of the CFT at strong coupling. We speculate that the kinetic equations should be interpreted as a holographic dual of the equation of motion of the collapsing shell.

Brane-antibrane systems at finite temperature and the entropy of black branes

We consider D-brane--anti-D-brane systems at T > 0. Starting at the closed string vacuum, we argue that a finite temperature leads to the reappearance of open string degrees of freedom. We also show that, at a sufficiently large temperature, the open string vacuum becomes stable. Building upon this observation and previous work by Horowitz, Maldacena and Strominger, we formulate a microscopic brane-antibrane model for the non-extremal black three-brane in ten dimensions (as well as for the black two- and five-branes in eleven dimensions). Under reasonable assumptions, and using known results from the AdS/CFT correspondence, the microscopic entropy agrees with the supergravity result up to a factor of 2p/p+1, with p the dimension of the brane. The negative specific heat and pressure of the black brane have a simple interpretation in terms of brane-antibrane annihilation. We also find in the model states resembling black holes and other lower-dimensional black branes.

Random walks and the Hagedorn transition

We study details of the approach to the Hagedorn temperature in string theory in various static spacetime backgrounds. We show that the partition function for a single string at finite temperature is the torus amplitude restricted to unit winding around Euclidean time. We use worldsheet path integral to derive the statement that the the sum over random walks of the thermal scalar near the Hagedorn transition is precisely the image under a modular transformation of the sum over spatial configurations of a single highly excited string. We compute the radius of gyration of thermally excited strings in AdSD ? Sn. We show that the winding mode indicates an instability despite the AdS curvature at large radius, and that the negative mass squared decreases with decreasing AdS radius, much like the type 0 tachyon. We add further arguments to statements by Barb?n and Rabinovici, and by Adams et. al., that the Euclidean AdS black hole can thought of as a condensate of the thermal scalar. We use this to provide circumstantial evidence that the condensation of the thermal scalar decouples closed string modes.

Newtonian Gravitons and D-brane Collective Coordinates in Wound String Theory

Recently it was shown that NCOS theories are part of a ten-dimensional theory known as Non-relativistic Wound string theory. We clarify the sense in which gravity is present in this theory. We show that Wound string theory contains exceptional unwound strings, including a graviton, which mediate the previously discovered instantaneous long-range interactions, but are negligible as asymptotic states. Unwound strings also provide the expected collective coordinates for the transverse D-branes in the theory. These and other results are shown to follow both from a direct analysis of the effect of the NCOS limit on the parent string theory, and from the worldsheet formalism developed by Gomis and Ooguri, about which we make some additional remarks. We also devote some attention to supergravity duals, and in particular show that the open and closed strings of the theory are respectively described by short and long strings on the supergravity side.

D3-brane holography

It has recently been conjectured that the AdS5/SYM4 correspondence can be generalized away from the conformal limit, to a duality between supergravity on the full asymptotically flat three-brane background and a theory characterized as N = 4 SYM deformed in the IR by a specific dimension-eight operator. Assuming that this relation is valid, we derive a prescription for computing n-point correlation functions in the holographic theory, which reduces to the standard AdS/CFT recipe at low energies. One- and two-point functions are discussed in detail. The prescription follows from very simple considerations and appears to be applicable to any asymptotically flat background. We also compute the quark-antiquark potential and comment on the description of the baryon in the supergravity picture. We conclude with some comments on the possible relation between our work and recent results in non-commutative field theories.

Planar diagrams in light-cone gauge

We consider the open string vacuum amplitude determining the interaction between a stack of N D3-branes and a single probe brane. When using light cone gauge, it is clear that the sum of planar diagrams (relevant in the large-N limit) is described by the free propagation of a closed string. A naive calculation suggests that the Hamiltonian of the closed string is of the form H = H0−gsN. The same form of the Hamiltonian follows from considering the bosonic part of the closed string action propagating in the full D3-brane background suggesting the naive calculation captures the correct information. Further, we compute explicitly from the open string side in the bosonic sector and show that, in a certain limit, the result agrees with the closed string expectations up to extra terms due to the fact that we ignored the fermionic sector. We briefly discuss extensions of the results to the superstring and to the sum of planar diagrams in field theory. In particular we argue that the calculations seem valid whenever one can define a (σ↔τ) dual Hamiltonian in the world-sheet which in principle does not require the existence of a string action. This seems more generic than the existence of a string dual in the large-N limit.

GRAVITON SCATTERING IN AN M-ORIENTIFOLD BACKGROUND

Abstract In this paper we study the scattering of gravitons off a five-orientifold in eleven dimensions. We compare the supergravity result with a two-loop M(atrix) model calculation and find exact agreement. The supergravity calculation involves non-linear three-graviton effects.