Joanna L. Karczmarek

The Gravity Dual of a Density Matrix

For a state in a quantum field theory on some spacetime, we can associate a density matrix to any subset of a given spacelike slice by tracing out the remaining degrees of freedom. In the context of the AdS/CFT correspondence, if the original state has a dual bulk spacetime with a good classical description, it is natural to ask how much information about the bulk spacetime is carried by the density matrix for such a subset of field theory degrees of freedom. In this note, we provide several constraints on the largest region that can be fully reconstructed, and discuss specific proposals for the geometric construction of this dual region.

Nonlocal field theories and their gravity duals

The gravity duals of nonlocal field theories in the large-N limit exhibit a novel behavior near the boundary. To explore this, we present and study the duals of dipole theories, a particular class of nonlocal theories with fundamental dipole fields. The nonlocal interactions are manifest in the metric of the gravity dual, and type-0 string theories make a surprising appearance. We compare the situation to that in noncommutative super-Yang-Mills theory.

Rindler Quantum Gravity

In this note, we explain how asymptotically globally AdS spacetimes can be given an alternate dual description as entangled states of a pair of hyperbolic space CFTs, which are associated with complementary Rindler wedges of the AdS geometry. The reduced density matrix encoding the state of the degrees of freedom in one of these CFTs describes the physics in a single wedge, which we can think of as the region of spacetime accessible to an accelerated observer in AdS. For pure AdS, this density matrix is thermal, and we argue that the microstates in this thermal ensemble correspond to spacetimes that are almost indistinguishable from a Rindler wedge of pure AdS away from the horizon, but with the horizon replaced by some kind of singularity where the geometrical description breaks down. This alternate description of AdS, based on patches associated with particular observers, may give insight into the holographic description of cosmologies where no observer has access to the full spacetime.

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.

Closed string tachyon condensation at c = 1

The c = 1 matrix model, with or without a type 0 hat, has an exact quantum solution corresponding to closed string tachyon condensation along a null surface. The condensation occurs, and spacetime dissolves, at a finite retarded time on +. The outgoing quantum state of tachyon fluctuations in this time-dependent background is computed using both the collective field and exact fermion pictures. Perturbative particle production induced by the moving tachyon wall is shown to be similar to that induced by a soft moving mirror. Hence, despite the fact that + for the tachyon is geodesicaly incomplete, quantum correlations in the incoming state are unitarily transmitted to the outgoing state in perturbation theory. It is also shown that, non-perturbatively, information can leak across the tachyon wall, and tachyon scattering is not unitary. Exact unitarity remains intact only in the free fermion picture.

Holographic entanglement entropy in nonlocal theories

A bstractWe compute holographic entanglement entropy in two strongly coupled non-local field theories: the dipole and the noncommutative deformations of SYM theory. We find that entanglement entropy in the dipole theory follows a volume law for regions smaller than the length scale of nonlocality and has a smooth cross-over to an area law for larger regions. In contrast, in the noncommutative theory the entanglement entropy follows a volume law for up to a critical length scale at which a phase transition to an area law occurs. The critical length scale increases as the UV cutoff is raised, which is indicative of UV/IR mixing and implies that entanglement entropy in the noncommutative theory follows a volume law for arbitrary large regions when the size of the region is fixed as the UV cutoff is removed to infinity. Comparison of behaviour between these two theories allows us to explain the origin of the volume law. Since our holographic duals are not asymptotically AdS, minimal area surfaces used to compute holographic entanglement entropy have novel behaviours near the boundary of the dual spacetime. We discuss implications of our results on the scrambling (thermalization) behaviour of these nonlocal field theories.

Hartle-Hawking Vacuum for C=1 Tachyon Condensation

Quantum vacua are constructed for a time-symmetric cosmology describing closed string tachyon condensation in two-dimensional string theory. Due to the euclidean periodicity of the solution, and despite its time dependence, we are able to construct thermal states at discrete values of the temperature. The asymptotic thermal Green functions and stress energy tensor are computed and found to have an intriguing resemblance to those in the Hartle-Hawking vacuum of a black hole.

Spacelike boundaries from the c = 1 matrix model

We find classical solutions of two dimensional noncritical string theory which give rise to geometries with spacelike boundaries, similar to spacetimes with cosmological event horizons. In the c=1 matrix model, these solutions have a representation as simple time-dependent configurations. We obtain the causal structure of the resulting spacetimes. Using the macroscopic loop transform, we probe the form of the tachyon condensate in the asymptotic regions.

Entanglement entropy on the fuzzy sphere

A bstractWe obtain entanglement entropy on the noncommutative (fuzzy) two-sphere. To define a subregion with a well defined boundary in this geometry, we use the symbol map between elements of the noncommutative algebra and functions on the sphere. We find that entanglement entropy is not proportional to the length of the region’s boundary. Rather, in agreement with holographic predictions, it is extensive for regions whose area is a small (but fixed) fraction of the total area of the sphere. This is true even in the limit of small noncommutativity. We also find that entanglement entropy grows linearly with N, where N is the size of the irreducible representation of SU(2) used to define the fuzzy sphere.

Hot giant loop holography

We argue that there is a phase transition in the expectation value of the Polyakov loop operator in the large