A Matrix Model for AdS2
A matrix quantum mechanics with potential $V={q^2 \over r^2}$ and an SL(2,R) conformal symmetry is conjectured to be dual to two-dimensional type 0A string theory on AdS$_2$ with $q$ units of RR flux.
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arXiv subjects
Andrew Strominger
Publications and source records attributed to Andrew Strominger.
Matrix Cosmology
Exact time-dependent solutions of c=1 string theory are described using the free fermion formulation. One such class of solutions describes draining of the Fermi sea and has a spacetime interpretation as closed string tachyon condensation. A second class of solutions, corresponding to droplets of Fermi liquid orbiting in phase space, describes closed cosmologies which bounce through singularities.
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UV Finite Brane Decay
The decay of an unstable D-brane via closed string emission and open string pair production is considered in subcritical string theory with a spacelike linear dilaton. The decay rate is given by the imaginary part of the annulus, which has ambiguities corresponding to the choices of incoming closed and open string vacua. An exact expression for the full annulus diagram is computed with a natural choice of incoming vacua. It is found that the ultraviolet divergences present in critical string theory in both of these processes are absent for any nonzero spacelike dilaton. Implications for the vexing issue of the tachyon dust are discussed.
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Nonlinear Instantons from Supersymmetric p-Branes
Supersymmetric configurations of type II D-branes with nonzero gauge field strengths in general supersymmetric backgrounds with nonzero B fields are analyzed using the kappa-symmetric worldvolume action. It is found in dimension four or greater that the usual instanton equation for the gauge field obtains a nonlinear deformation. The deformation is parameterized by the topological data of the B-field, the background geometry and the cycle wrapped by the brane. In the appropriate dimensions, limits and settings these equations reduce to deformed instanton equations recently found in the context of noncommutative geometry as well as those following from Lagrangians based on Bott-Chern forms. We further consider instantons comprised of M5-branes wrapping a Calabi-Yau space with non-vanishing three-form field strengths. It is shown that the instanton equations for the three-form are related to the Kodaira-Spencer equations.
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A Quantum Bousso Bound
The Bousso bound requires that one quarter the area of a closed codimension two spacelike surface exceeds the entropy flux across a certain lightsheet terminating on the surface. The bound can be violated by quantum effects such as Hawking radiation. It is proposed that at the quantum level the bound be modified by adding to the area the quantum entanglement entropy across the surface. The validity of this quantum Bousso bound is proven in a two-dimensional large N dilaton gravity theory.
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S-Brane Thermodynamics
The description of string-theoretic s-branes at g_s=0 as exact worldsheet CFTs with a (lambda cosh X^0) or (lambda e^(X^0)) boundary interaction is considered. Due to the imaginary-time periodicity of the interaction under X^0 -> X^0 + 2 pi i, these configurations have intriguing similarities to black hole or de Sitter geometries. For example, the open string pair production as seen by an Unruh detector is thermal at temperature T = 1/4 pi. It is shown that, despite the rapid time dependence of the s-brane, there exists an exactly thermal mixed state of open strings. The corresponding boundary state is constructed for both the bosonic and superstring cases. This state defines a long-distance Euclidean effective field theory whose light modes are confined to the s-brane. At the critical value of the coupling lambda=1/2, the boundary interaction simply generates an SU(2) rotation by pi from Neumman to Dirichlet boundary conditions. The lambda=1/2 s-brane reduces to an array of sD-branes (D-branes with a transverse time dimension) on the imaginary time axis. The long range force between a (bosonic) sD-brane and an ordinary D-brane is shown from the annulus diagram to be 11/12 times the force between two D-branes. The linearized time-dependent RR field F=dC produced by an sD-brane in superstring theory is explicitly computed and found to carry a half unit of s-charge Q_s=\int_S *F=1/2, where S is any transverse spacelike slice.
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Open String Creation by S-Branes
An sp-brane can be viewed as the creation and decay of an unstable D(p+1)-brane. It is argued that the decaying half of an sp-brane can be described by a variant of boundary Liouville theory. The pair creation of open strings by a decaying s-brane is studied in the minisuperspace approximation to the Liouville theory. In this approximation a Hagedorn-like divergence is found in the pair creation rate, suggesting the s-brane energy is rapidly transferred into closed string radiation.
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Spacelike Branes
Scalar field theories with appropriate potentials in Minkowski space can have time-dependent classical solutions containing topological defects which correspond to S-branes - i.e. branes all of whose tangential dimensions are spacelike. It is argued that such S-branes arise in string theory as time-dependent solutions of the worldvolume tachyon field of an unstable D-brane or D-brane-anti-D-brane pair. Using the known coupling of the spacetime RR fields to the worldvolume tachyon it is shown that these S-branes carry a charge, defined as the integral of a RR field strength over a sphere (containing a time as well as spatial dimensions) surrounding the S-brane. This same charge is carried by SD-branes, i.e. Dirichlet branes arising from open string worldsheet conformal field theories with a Dirichlet boundary condition on the timelike dimension. The corresponding SD-brane boundary state is constructed. Supergravity solutions carrying the same charges are also found for a few cases.
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Superconformal Multi-Black Hole Moduli Spaces in Four Dimensions
Quantum mechanics on the moduli space of N supersymmetric Reissner-Nordstrom black holes is shown to admit 4 supersymmetries using an unconventional supermultiplet which contains 3N bosons and 4N fermions. A near-horizon limit is found in which the quantum mechanics of widely separated black holes decouples from that of strongly-interacting, near-coincident black holes. This near-horizon theory is shown to have an enhanced D(2,1;0) superconformal symmetry. The bosonic symmetries are SL(2,R) conformal symmetry and SU(2)xSU(2) R-symmetry arising from spatial rotations and the R-symmetry of N=2 supergravity.
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de Sitter Space in Non-Critical String Theory
Supercritical string theories in D>10 dimensions with no moduli are described, generalizing the asymmetric orientifold construction of one of the authors. By taking the number of dimensions to be large and turning on fluxes, dilaton potentials are generated with nontrivial minima at arbitrarily small cosmological constant and D-dimensional string coupling, separated by a barrier from a flat-space linear dilaton region, but possibly suffering from strong coupling problems. The general issue of the decay of a de Sitter vacuum to flat space is discussed. For relatively small barriers, such decays are described by gravitational instantons. It is shown that for a sufficiently large potential barrier, the bubble wall crosses the horizon. At the same time the instanton decay time exceeds the Poincare recurrence time. It is argued that the inclusion of such instantons is neither physically meaningful nor consistent with basic principles such as causality. This raises the possibility that such de Sitter vacua are effectively stable. In the case of the supercritical flux models, decays to the linear dilaton region can be forbidden by such large barriers, but decays to lower flux vacua including AdS minima nevertheless proceed consistently with this criterion. These models provide concrete examples in which cosmological constant reduction by flux relaxation can be explored.
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PP-Wave / CFT_2 Duality
We investigate the pp-wave limit of the AdS_3\times S^3\times K3 compactification of Type IIB string theory from the point of view of the dual Sym_N(K3) CFT. It is proposed that a fundamental string in this pp-wave geometry is dual to the c=6 effective string of the Sym_N(K3) CFT, with the string bits of the latter being composed of twist operators. The massive fundamental string oscillators correspond to certain twisted Virasoro generators in the effective string. It is shown that both the ground states and the genus expansion parameter (at least in the orbifold limit of the CFT) coincide. Surprisingly the latter scales like J^2/N rather than the J^4/N^2 which might have been expected. We demonstrate a leading-order agreement between the pp-wave and CFT particle spectra. For a degenerate special case (one NS 5-brane) an intriguing complete agreement is found.
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Conformal Vacua and Entropy in de Sitter Space
The dS/CFT correspondence is illuminated through an analysis of massive scalar field theory in d-dimensional de Sitter space. We consider a one-parameter family of dS-invariant vacua related by Bogolyubov transformations and compute the corresponding Green functions. It is shown that none of these Green functions correspond to the one obtained by analytic continuation from AdS. Among this family of vacua are in (out) vacua which have no incoming (outgoing) particles on past (future) infinity. Surprisingly, it is shown that in odd spacetime dimensions the in and out vacua are the same, implying the absence of particle production for this state. The correlators of the boundary CFT, as defined by the dS/CFT correspondence, are shown to depend on the choice of vacuum state - the correlators with all points on past infinity vanish in the in vacuum. For dS_3 we argue that this bulk vacuum dependence of the correlators is dual to a deformation of the boundary CFT_2 by a specific marginal operator. It is also shown that Witten's non-standard de Sitter inner product (slightly modified) reduces to the standard inner product of the boundary field theory. Next we consider a scalar field in the Kerr-dS_3 Euclidean vacuum. A density matrix is constructed by tracing out over modes which are causally inaccessible to a single geodesic observer. This is shown to be a thermal state at the Kerr-dS_3 temperature and angular potential. It is further shown that, assuming Cardy's formula, the microscopic entropy of such a thermal state in the boundary CFT precisely equals the Bekenstein-Hawking value of one quarter the area of the Kerr-dS_3 horizon.
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Les Houches Lectures on De Sitter Space
These lectures present an elementary discussion of some background material relevant to the problem of de Sitter quantum gravity. The first two lectures discuss the classical geometry of de Sitter space and properties of quantum field theory on de Sitter space, especially the temperature and entropy of de Sitter space. The final lecture contains a pedagogical discussion of the appearance of the conformal group as an asymptotic symmetry group, which is central to the dS/CFT correspondence. A (previously lacking) derivation of asymptotically de Sitter boundary conditions is also given.
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Inflation and the dS/CFT Correspondence
It is speculated that the observed universe has a dual representation as renormalization group flow between two conformal fixed points of a three-dimensional Euclidean field theory. The infrared fixed point corresponds to the inflationary phase in the far past. The ultraviolet fixed point corresponds to a de Sitter phase dominated by the cosmological constant indicated in recent astronomical data. The monotonic decrease of the Hubble parameter corresponds to the irreversibility of renormalization group flow.
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Two-Black-Hole Bound States
The quantum mechanics of $N$ slowly-moving BPS black holes in five dimensions is considered. A divergent continuum of states describing arbitrarily closely bound black holes with arbitrarily small excitation energies is found. A superconformal structure appears at low energies and can be used to define an index counting the weighted number of supersymmetric bound states. It is shown that the index is determined from the dimensions of certain cohomology classes on the symmetric product of $N$ copies of $R^4$. An explicit computation for the case of N=2 with no angular momentum yields a finite nonzero result.
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The dS/CFT Correspondence
A holographic duality is proposed relating quantum gravity on dS_D (D-dimensional de Sitter space) to conformal field theory on a single S^{D-1} ((D-1)-sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on I^+ (the future boundary of dS_D) are mapped to the antipodal points on S^{D-1} relative to those on I^-. For the case of dS_3, which is analyzed in some detail, the central charge of the CFT_2 is computed in an analysis of the asymptotic symmetry group at I^\pm. This dS/CFT proposal is supported by the computation of correlation functions of a massive scalar field. In general the dual CFT may be non-unitary and (if for example there are sufficently massive stable scalars) contain complex conformal weights. We also consider the physical region O^- of dS_3 corresponding to the causal past of a timelike observer, whose holographic dual lives on a plane rather than a sphere. O^- can be foliated by asymptotically flat spacelike slices. Time evolution along these slices is generated by L_0+\bar L_0, and is dual to scale transformations in the boundary CFT_2.
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Spinning Bound States of Two and Three Black Holes
Bound states of BPS particles in five-dimensional N=2 supergravity are counted by a topological index. We compute this bound state index exactly for two and three black holes as a function of the SU(2)_L angular momentum. The required regulator for the infrared continuum of near-coincident black holes is chosen in accord with the enhanced superconformal symmetry.
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Fluxbranes in String Theory
A flux p-brane in D dimensions has (p+1)-dimensional Poincare invariance and a nonzero rank (D-p-1) field strength tangent to the transverse dimensions. We find a family of such solutions in string theory and M-theory and investigate their properties.
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