Quantum and Gravitational Theory Group

September 14, 2020

"Maximum Observable Blueshift from Circular Equatorial Kerr Orbiters"

Abstract: The region of spacetime near the event horizon of a black hole can be viewed as a deep potential well at large gravitational redshift relative to distant observers. However, matter orbiting in this region travels at relativistic speeds and can impart a significant Doppler shift to its electromagnetic emission, sometimes resulting in a net observed blueshift at infinity. In this talk we investigate emission produced by isotropic monochromatic emitters on circular equatorial orbits around a Kerr black hole, and obtain simple relations describing how the maximum blueshift encodes black hole spin and inclination. We find that small values of the maximum blueshift yield an excellent probe of inclination, while larger values provide strong constraints on spin or inclination in terms of the other.

September 21, 2020

"Leading order corrections to the quantum extremal surface prescription"

Abstract: We show that a naïve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at leading order than the minimal QES), together with a large amount of highly incompressible bulk entropy between the two surfaces. We trace the source of the corrections to a failure of the assumptions used in the replica trick derivation of the QES prescription, and show that a more careful derivation correctly computes the corrections. Using tools from one-shot quantum Shannon theory (smooth min- and max-entropies), we generalize these results to a set of refined conditions that determine whether the QES prescription holds. We find similar refinements to the conditions needed for entanglement wedge reconstruction (EWR), and show how EWR can be reinterpreted as the task of one-shot quantum state merging (using zero-bits rather than classical bits), a task gravity is able to achieve optimally efficiently.

September 30, 2020

*Please note that this seminar takes place on a Wednesday (Brandeis Monday)

"The Page Curve for Reflected Entropy"

Abstract: Reflected Entropy is a bipartite correlation measure with a simple geometric holographic dual, the minimal entanglement wedge cross section. This duality further motivates the idea that spacetime emerges from entanglement. Further, it illustrates the richness of the multipartite entanglement structure of holographic systems. A particularly interesting feature that we focus on in this talk is the phase transition between a connected and disconnected entanglement wedge where the reflected entropy jumps discontinuously. We explain how this phase transition is resolved in random tensor networks which serve as toy models for holography. This argument based on the replica trick motivates a general ansatz for the mechanism of the phase transition in AdS/CFT.

October 5, 2020

"Heavy Operators and Hydrodynamic Tails"

Abstract: The late time physics of interacting QFTs at finite temperature is controlled by hydrodynamics. For CFTs this implies that heavy operators -- which are generically expected to create thermal states -- can be studied semiclassically. We show that hydrodynamics universally fixes the OPE coefficients C_{HH'L}, on average, of all neutral light operators with two non-identical heavy ones, as a function of the scaling dimension and spin of the operators. These methods can be straightforwardly extended to CFTs with global symmetries, and generalize recent EFT results on large charge operators away from the case of minimal dimension at fixed charge. I will also revisit certain aspects of late time thermal correlators in QFT and other diffusive systems.

October 12, 2020

"Entropic order parameters for symmetries in QFT"

Abstract: In QFT there is an algebra of operators attached to any spacetime region. Simple degradations of the most harmonious possible relation between algebras and regions are shown to encode generalized symmetries. Nets of algebras with these symmetries allow for a non uniqueness of the algebras that can be assigned to a given region. This non uniqueness suggests a simple geometrical order parameter in terms of a relative entropy. These satisfy a ''certainty relation'' connecting the statistics of the order and disorder parameters for complementary regions. We describe how the lore about phases of theories with generalized symmetries is seen in this new picture.

October 19, 2020

"The Schottky Anomaly of de Sitter Black Holes"

Abstract: Black holes with Λ > 0 (SdS) have fascinating properties that are distinct from the asymptotically flat or AdS cases, starting with the fact that there are two horizons in the spacetime, one black hole and one cosmological. The two horizons have different temperatures and the total gravitational entropy is the sum of the horizon areas. As a result, both the mass M and entropy S are bounded between minimum and maximum values. Intriguingly, there is an extremum in the specific heat ∂M/∂Tb as well as in the curve ∂S/∂Tb, which resemble the Schottky anomaly of a two level system in statistical mechanics. In this talk we investigate classical and quantum mechanical features of SdS thermodynamics that make it resemble the physics of a paramagnet. We start by showing that the Schottky behavior is to be expected for classical fluctuations based on the first laws for SdS black holes. Second, we present calculations of black hole and cosmological particle production in SdS and find that the quantum fluctuations share the behavior of classical ones.

November 2, 2020

"Quantum error correction and large N"

Abstract: In recent years quantum error correction(QEC) has become an important part of AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems. The purpose of this talk is to fill this gap by studying the error correcting properties of the fermionic sector of various large N theories. Specifically we examine SU(N) matrix quantum mechanics and 3-rank tensor O(N)^3theories. Both of these theories contain large gauge groups. We argue that gauge singlet states indeed form a quantum error correcting code. Our considerations are based purely on large N analysis and do not appeal to a particular form of Hamiltonian or holography.

November 9, 2020

"Wess-Zumino-Witten terms and the geometry and topology of lattice systems"

Abstract: Wess-Zumino-Witten terms are topologically-nontrivial terms in the effective actions which arise from integrating out short-distance degrees of freedom which couple of slowly-varying scalar fields. They can be viewed as higher-dimensional generalizations of the Berry connection. This viewpoint suggests that WZW terms encode the non-trivial topology of the space of massive field theories and should arise also in the context of gapped lattice systems. I will explain how to compute WZW terms for a family of gapped lattice systems in d spatial dimensions. The answer suggests an important role for coarse geometry as introduced by J. Roe.

November 16, 2020

November 23, 2020

"Constraints on Tree Level Gravitational Scattering"

Abstract: Motiviated by a combination of the Chaos bound and AdS/CFT, we conjecture that all classical theories that give rise to S matrices that grow faster than s^2 in the Regge limit are unphysical. We then present a complete and exhaustive classification of all kinematically allowed exchange and contact S matrices (assuming that the vertices that generate the contact diagrams are polynomial in momenta and that no more than a finite number of intermediate particles are exchanged) and demonstrate that the only classical S matrix obeying these constraints and also the conjectured bound on Regge scattering in six or lower spacetime dimensions is the Einstein S matrix.

November 30, 2020

"Towards Emergent Gravity in Approximate Quantum Error Correction Codes"

Abstract: It is known that the AdS/CFT correspondence is related to approximate quantum error correction codes. However, the exact manner in which gravity can arise in such codes remains largely unexplored. Here we construct an approximate quantum error correction code which can be represented as a holographic tensor network. In the "noiseless" limit, it admits a local log-depth decoding circuit and reproduces certain properties of holography, such as the Ryu-Takayanagi formula and subregion duality, much like other known holographic codes. However, the code becomes approximate when "coherent noise" is injected, allowing it to capture features analogous to those of gravity, such as back-reaction, subspace-dependence, and approximate bulk locality. I will explain how these features are manifested in the tensor network.