Quantum and Gravitational Theory Group

January 17, 2023

January 24, 2023

Title: Quantum dimer models in the age of Rydberg quantum simulators 

Abstract: Strongly interacting arrays of Rydberg atoms provide versatile platforms for exploring exotic many-body phases and dynamics of correlated quantum systems. Motivated by recent experimental advances, we investigate the quantum phases that can be realized by such Rydberg atom simulators in two dimensions. We show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to constrained dimer models and emergent Z₂ gauge theories endowed with matter fields. Based on this mapping, we demonstrate how Rydberg platforms can be used to realize topological spin liquid states based solely on their native van der Waals interactions. We also discuss the nature of the fractionalized excitations of two distinct classes of such Z₂ quantum spin liquid states and illustrate their rich interplay with proximate solid phases.

 

*Note: This week the seminar will be held in Abelson 229

January 31, 2023

Title: Maximal Entangling Rates from Holography

Abstract: We prove novel speed limits on the growth of entanglement, equal time correlators, and spacelike Wilson loops in spatially uniform time-evolving states in strongly coupled CFTs with holographic duals. These bounds can also be viewed as quantum weak energy conditions. Several of the speed limits are valid for regions of arbitrary size and with multiple connected components, and our findings imply new bounds on the effective entanglement velocity of small subregions. In 2d CFT, our results prove a conjecture by Liu and Suh for a large class of states. Key to our findings is a momentum-entanglement correspondence, showing that entanglement growth is computed by the momentum crossing the HRT surface. In our setup, we prove a number of general features of boundary-anchored extremal surfaces, such as a sharp bound on the smallest radius that a surface can probe, and that the tips of extremal surfaces cannot lie in trapped regions. Our methods rely on novel global GR techniques, including a delicate interplay between Lorentzian and Riemannian Hawking masses. While our proofs assume the dominant energy condition in the bulk, we provide numerical evidence that our bounds are true under less restrictive assumptions.

*Note: This week the seminar will be held in Abelson 229

February 7, 2023

Title: JT gravity with matter, generalized ETH, and Random Matrices

Abstract: The Eigenstate Thermalization Hypothesis (ETH) asserts that at sufficiently late times, chaotic many-body quantum theories may be described statistically. We consider an ensemble defined by a single-trace two-matrix model, where one matrix represents the Hamiltonian and the other represents a simple operator. The matrix potential is chosen such that the disk correlators of the matrix model agree with the disk correlators of JT gravity minimally coupled to a massive free scalar field. We compute cylinder correlators in the matrix model, which correspond to wormhole amplitudes in the dual gravity theory. We also comment on how our construction could be generalized to statistical models of higher-dimensional holographic CFTs. The ensemble must be constrained to respect the large-N algebra of the light operators.

February 14, 2023

Title: String Theory in Off-shell Backgrounds: The Sphere Partition Function and Black Hole Entropy.

Abstract: The worldsheet theory of string backgrounds is a CFT with zero central charge. This is the definition of on-shell string theory. In off-shell string theory, on the other hand, conformal invariance on the worldsheet is explicitly broken, and the worldsheet theory is therefore a QFT with a UV cutoff.
In the first part of the talk, I will explain Arkady Tseytlin’s prescriptions for constructing classical (tree-level) off-shell effective actions and provide a general proof, using conformal perturbation theory, that it gives the correct equations of motion, to all orders in perturbation theory and α′. I will also show how the off-shell prescriptions are equivalent to quotienting out by the gauge orbits of a regulated moduli space with operator insertions.
In the second part of the talk, I will explain the underlying conceptual structure of the Susskind and Uglum black hole entropy calculation. I will show how the classical (tree-level) effective action and entropy S = A/4G_N can be calculated from the sphere diagrams.
Time permitting, I will discuss ongoing work on a stringy derivation of the holographic entanglement entropy (the RT formula).

February 21, 2023

February 28, 2023

Title: Non-Invertible Symmetries in Supergravity.

Abstract: I discuss the existence of non-invertible symmetries in 11d and 10d maximal Supergravity. These symmetries should be broken or gauged by the UV completion. We will see that the presence of D-branes in String Theory explicitly breaks them.

March 7, 2023

Title: Recent Progress in Quantum Gravity

Abstract: The structure of the bulk Hilbert space in quantum gravity is very different from standard quantum field theory. An illustration of this assertion is the well-known holographic principle which states that the dimension of the Hilbert space of a gravitational region scales with its boundary area instead of the volume. Mathematically, this is described by the fact that the diffeomorphism invariance enforces a dressing of any local bulk operator by a gravitational Wilson line to a place where gravity can be decoupled (in the absence of any diffeomorphism breaking background configurations). This has significant implications for the fine-structure of the states in the Hilbert space in quantum gravity, for example there is no factorization of the Hilbert space of a gravitational region into subregions which is nevertheless the usual starting point to study entanglement properties of Hilbert space states in quantum field theories. Misunderstanding of this special property of quantum gravity constantly causes puzzles such as Hawking's famous black hole information paradox and the AMPS firewall paradox. The recent progress in the understanding of the brandly new emergent concept- entanglement island sheds light on these questions in quantum gravity. In this talk, I'll give a quick review of Hawking's information paradox, the AMPS firewall paradox and their resolution in the Karch-Randall braneworld by the emergence of entanglement island then I'll discuss the implications to these paradoxes and quantum gravity in general from the physics of the Karch-Randall braneworld.

March 14, 2023

Title: Long Time Limits of Generalized Ricci Flow

Abstract: We derive rigidity results for generalized Ricci flow blowdown limits on classes of nilpotent principal bundles. We accomplish this by constructing new functionals over the base manifold that are monotone along the flow. This overcomes a major hurdle in the nonabelian theory where the expected Perelman-type functionals are not monotone and do not yield results. Our functionals were inspired and built from subsolutions of the heat equation, which we discovered using the nilpotency of the structure group and the flow equations. We also use these and other new subsolutions to prove that, given initial data, the flow exists on the principal bundle for all positive time and satisfies type III decay bounds. In future work, we will apply these results to study the collapsing of generalized Ricci flow solutions and to classify type III pluriclosed flows on complex surfaces.

March 21, 2023

Title: Quenching the Black Hole Zoo

Abstract: Many properties of black holes, such as their entropy, are universal; this suggests that there is a commonality in their statistical description. In this talk, I will discuss non-universal aspects of near-extremal black holes in 4D N=2 SUGRA, which are encoded in deformations away from an idealized AdS_2 geometry. Such features are important to understand in order to construct a microscopic dual of (the near-horizon region of) near-extremal black holes. I will discuss an interesting pathology that appears for certain backgrounds: the entropy as computed from the on-shell action can become negative. I will argue that this pathology can be resolved within the regime of semiclassical gravity by considering quenched instead of annealed quantities.

March 21, 2023

Title: Is the extensive mutual information model a QFT?

Abstract: I will introduce the so-called extensive mutual information model (EMI), which is the unique solution to the known axioms of the ground state mutual information of a CFT, when one imposes extensivity on its arguments. Using various results concerning the mutual information of largely separated regions, I will then show that the EMI cannot describe the ground state mutual information of a CFT in dimensions greater than two. This result suggests that the set of known axioms of the mutual information might be incomplete.

 

**Note that this seminar will take place at 4pm**

March 28, 2023

Title: Entwinement and bulk reconstruction in AdS3/CFT2

Abstract: A nice setup to investigate subtle aspects of how spacetime emerges from the internal degrees of freedom in holographic theories is provided by AdS3/CFT2 holography. There, quotients of AdS3 with conical singularities possess several extremal "surfaces" (curves in D=3) anchored to a fixed boundary region. The length of those curves which are extremal but non-minimal was conjectured in the past to compute some loosely defined notion of entanglement between internal degrees of freedom in the dual CFT. This quantity was dubbed "entwinement". In this talk, I will give a more precise picture of how entwinement can be defined for the setup relevant to AdS3/CFT2 holography, in which the field theory is a symmetric product orbifold CFT. In the process, it will become clear that this notion is indeed what the lengths of extremal but non-minimal curves are computing. Time permitting, I will also put forward some more speculative questions related to the general program of bulk reconstruction that can be discussed in the setup of quotient geometries in AdS3/CFT2.

April 4, 2023

Title: Horizon Scattering, Partition Functions, and Edge Modes

Abstract: Ideal gas thermal canonical partition functions for quantum fields outside (inside) a black hole (de Sitter) horizon are ill-defined due to an infinite density of normal modes originating from the continuous nature of the spectrum. In this talk, I will explain how to make sense of this computation by viewing the Lorentzian field equation in a black hole background as an effective 1D scattering problem. The scattering phases encode non-trivial information about the single-particle density of states (DOS) and can be extracted by ``renormalizing" the DOS with respect to a reference DOS. This defines a renormalized thermal free energy up to a choice of reference. Interestingly, we discover that the 1-loop Euclidean path integral, as computed by the Denef-Hartnoll-Sachdev (DHS) formula, fixes the reference free energy to be that on a Rindler-like region. Time permitting, I will explain how extending the DHS argument to spinning fields allows us to unambiguously identify a bulk-edge split for their Euclidean partition functions. The bulk part captures the renormalized thermal free energy described above, while the edge part is related to quasinormal modes that fail to analytically continue to a subset of Euclidean modes with enhanced fall-offs near the origin.

April 11, 2023

April 18, 2023

Title: Entanglement entropies for Lifshitz fermionic fields at finite density

Abstract: The entanglement entropies of an interval for the free fermionic spinless Schroedinger field theory at finite density and zero temperature are investigated. The interval is either on the line or at the beginning of the half line, when either Neumann or Dirichlet boundary conditions are imposed at the origin. We show that the entanglement entropies are finite functions of a dimensionless parameter proportional to the area of the rectangular region in the phase space identified by the Fermi momentum and the length of the interval.
For the interval on the line, the entanglement entropy is a monotonically increasing function. Instead, for the interval on the half line, it displays an oscillatory behaviour related to the Friedel oscillations of the mean particle density at the entangling point.
By employing the properties of the prolate spheroidal wave functions or the expansions of the tau functions of the kernels occurring in the spectral problems, determined by the two point function, we find analytic expressions for the expansions of the entanglement entropies in the asymptotic regimes of small and large area of the rectangular phase space region. Extending our analysis to a class of free fermionic Lifshitz models, we find that the parity of the Lifshitz exponent determines the properties of the bipartite entanglement.

April 25, 2023

Title: Spaces of QFTs and tameness

Abstract: I will discuss the notion of a space of quantum field theories, and explain various approaches to its definition and some of its expected properties.

I will then cover joint work with Thomas Grimm and Lorenz Schlechter on tameness of quantum field theories. This is based on the mathematical concept of o-minimal structures which has been very powerful for proving finiteness results. Given a QFT or a space of QFTs, we define a corresponding structure, and conjecture in many cases that it is tame (o-minimal). We also show that Feynman amplitudes at any fixed loop order
are tame.

May 2, 2023

May 23, 2023

Title:
The cosmological switchback effect

Abstract:
The volume behind the black hole horizon was suggested as a holographic dual for the quantum computational complexity of the boundary state in AdS/CFT. This identification is strongly motivated by the switchback effect: a characteristic delay of complexity growth in reaction to an inserted perturbation, modelled as a shockwave in the bulk. Recent proposals of de Sitter (dS) holography suggest that a dual theory could be living on a stretched horizon near the cosmological horizon.

In this talk, I will show how the spacetime volume behind the cosmological horizon in Schwarzschild-dS space reacts to the insertion of shockwaves in an attempt to characterize the properties of this dual theory. I will demonstrate that a switchback effect can be observed in dS space. That is, the growth of complexity is delayed in reaction to a perturbation. This delay is longer for earlier shocks and depends on a scrambling time which is logarithmic in the strength of the shockwave and proportional to the inverse temperature of the cosmological dS horizon. This behavior is very similar to what happens for AdS black holes, albeit the geometric origin of the effect is different.