Large N Fractons.

We consider theories of N-component fields with exotic spacetime symmetries, including a conserved dipole moment. Microscopic charges are immobile by symmetry, and so resemble fractons. Using collective fields we solve these models to leading order in large N. The large N solution reveals that these models are strongly correlated, and that interactions dress the microscopic charges so that they become mobile, long-lived quasiparticles. Dipole symmetry is spontaneously broken throughout the phase diagram of these models, leading to a low-energy Goldstone description.

Isometric Evolution in de Sitter Quantum Gravity.

We study time evolution in a simple model of de Sitter quantum gravity, namely, Jackiw-Teitelboim with a positive cosmological constant. We find that time evolution is isometric rather than unitary. The states that are projected out under time evolution correspond to initial conditions that crunch. Our findings suggest that knowledge of bulk physics, even on arbitrarily large timescales, is insufficient to deduce the de Sitter S matrix.

From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects.

We study whether the relations between the Weyl anomaly, entanglement entropy (EE), and thermal entropy of a two-dimensional (2D) conformal field theory (CFT) extend to 2D boundaries of 3D CFTs, or 2D defects of D≥3 CFTs. The Weyl anomaly of a 2D boundary or defect defines two or three central charges, respectively. One of these, b, obeys a c theorem, as in 2D CFT. For a 2D defect, we show that another, d_{2}, interpreted as the defect's "conformal dimension," must be non-negative if the averaged null energy condition holds in the presence of the defect. We show that the EE of a sphere centered on a planar defect has a logarithmic contribution from the defect fixed by b and d_{2}. Using this and known holographic results, we compute b and d_{2} for 1/2-Bogomol'nyi-Prasad-Sommerfield surface operators in the maximally supersymmetric (SUSY) 4D and 6D CFTs. The results are consistent with b's c theorem. Via free field and holographic examples we show that no universal "Cardy formula" relates the central charges to thermal entropy.

Displacement Operators and Constraints on Boundary Central Charges.

Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in three- and four-dimensional conformal field theories in terms of two- and three-point correlation functions of the displacement operator. We provide a general derivation by comparing the trace anomaly with scale dependent contact terms in the correlation functions. We conjecture a relation between the a-type boundary charge in three dimensions and the stress tensor two-point function near the boundary. We check our results for several free theories.

Chaos in AdS_{2} Holography.

We revisit two-dimensional holography with the Sachdev-Ye-Kitaev models in mind. Our main result is to rewrite a generic theory of gravity near a two-dimensional anti-de Sitter spacetime throat as a novel hydrodynamics coupled to the correlation functions of a conformal quantum mechanics. This gives a prescription for the computation of n-point functions in the dual quantum mechanics. We thereby find that the dual is maximally chaotic.

Boundary Effective Action for Quantum Hall States.

We consider quantum Hall states on a space with boundary, focusing on the aspects of the edge physics which are completely determined by the symmetries of the problem. There are four distinct terms of Chern-Simons type that appear in the low-energy effective action of the state. Two of these protect gapless edge modes. They describe Hall conductance and, with some provisions, thermal Hall conductance. The remaining two, including the Wen-Zee term, which contributes to the Hall viscosity, do not protect gapless edge modes but are instead related to the local boundary response fixed by symmetries. We highlight some basic features of this response. It follows that the coefficient of the Wen-Zee term can change across an interface without closing a gap or breaking a symmetry.

Constraint on Defect and Boundary Renormalization Group Flows.

A conformal field theory (CFT) in dimension d≥3 coupled to a planar, two-dimensional, conformal defect is characterized in part by a "central charge" b that multiplies the Euler density in the defect's Weyl anomaly. For defect renormalization group flows, under which the bulk remains critical, we use reflection positivity to show that b must decrease or remain constant from the ultraviolet to the infrared. Our result applies also to a CFT in d=3 flat space with a planar boundary.

Holographic dual of an Einstein-Podolsky-Rosen pair has a wormhole.

We construct the holographic dual of two colored quasiparticles in maximally supersymmetric Yang-Mills theory entangled in a color singlet Einstein-Podolsky-Rosen (EPR) pair. In the holographic dual, the entanglement is encoded in a geometry of a nontraversable wormhole on the world sheet of the flux tube connecting the pair. This gives a simple example supporting the recent claim by Maldacena and Susskind that EPR pairs and nontraversable wormholes are equivalent descriptions of the same physics.

Towards hydrodynamics without an entropy current.

We present a generating functional which describes the equilibrium thermodynamic response of a relativistic system to external sources. A variational principle gives rise to constraints on the response parameters of relativistic hydrodynamics without making use of an entropy current. Our method reproduces and extends results available in the literature. It also provides a technique for efficiently computing n-point zero-frequency correlation functions within the hydrodynamic derivative expansion without the need to explicitly solve the equations of hydrodynamics.

Semiholographic quantum criticality.

We identify the near-critical effective theory (EFT) for a wide class of low-temperature phase transitions found via holography. The EFT is of the semiholographic type and describes both holographic Berezinskii-Kosterlitz-Thouless and second-order transitions with nontrivial scaling. It is a simple generalization of the Ginzburg-Landau-Wilson paradigm to systems with an emergent (or hidden) conformal sector. Having identified the near-critical EFT, we explore its basic phenomenology by computing critical exponents and low-frequency correlators.

Holographic Berezinskii-Kosterlitz-Thouless transitions.

We find the first example of a quantum Berenzinskii-Kosterlitz-Thouless (BKT) phase transition in two spatial dimensions via holography. This transition occurs in the D3/D5 system at nonzero density and magnetic field. At any nonzero temperature, the BKT scaling is destroyed and the transition becomes second order with mean-field exponents. We go on to conjecture about the generality of quantum BKT transitions in two spatial dimensions.