Quantum Fields and Strings

In the first part of the seminar I will give a short review of the frame-independent formulation of Newtonian gravity, called Newton-Cartan Gravity, and explain why there is a renewed interest into non-relativistic gravity in general.  In the second part I will discuss, as a particular application,  a recent proposal for an Effective Field Theory describing a massive spin-2 mode (the so-called GMP mode) in the Fractional Quantum Hall Effect.

Topological defect operators are extended operators in a quantum field theory (QFT) whose correlation functions are independent of continuous changes of the ambient space. They satisfy nontrivial fusion relations and put nontrivial constraints on the QFT itself and its deformations (such as renormalization group (RG) flows). Canonical examples of topological defect operators include generators of (higher-form) global symmetries whose constraints on the QFT have been well-studied. However they constitute just a tip of a much richer framework which we explore in detail in two spacetime dimensions. 

More specifically, we study the crossing relations of general topological defect lines (TDL) in two dimensions, discuss their relation to the usual 't Hooft anomalies associated to global symmetries, and use them to constrain RG flows to either conformal fixed points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.

States of a CFT's subregions are consistent with a given global state. For a holographic CFT, this amounts to different entanglement wedges being patches of the same geometry. What relations between them make this possible?

I will propose a Berry experiment to study this question. Berry introduced a connection to describe transformations induced by adiabatically varying Hamiltonians. I will introduce a connection to study how the zero modes of a modular Hamiltonian are affected by varying the CFT subregion that supplies it. I will explain the geometric meaning of modular Berry phases in the bulk and describe an experiment to measure them which involves observers moving with adiabatically varying accelerations. 

I derive a universal upper bound on the capacity of any communication channel between two distant systems. The Holevo quantity, and hence the mutual information, is at most of order EΔt/ℏ, where E the average energy of the signal, and Δt is the amount of time for which detectors operate. The bound does not depend on the size or mass of the emitting and receiving systems, nor on the nature of the signal. No restrictions on preparing and processing the signal are imposed. 
As an example, I consider the encoding of information in the transverse or angular position of a signal emitted and received by systems of arbitrarily large cross-section. In the limit of a large message space, quantum effects become important even if individual signals are classical, and the bound is upheld.

We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications.

All physical constraints of the conformal bootstrap in principle arise by applying linear functionals to the conformal bootstrap equation. An important goal of the bootstrap program is to identify a suitable basis for the space of functionals -- one that would allow us to solve crossing analytically. In my talk, I will describe two particularly convenient choices of the basis for the 1D conformal bootstrap. The two bases manifest the crossing symmetry of the four-point function of a generalized free boson and generalized free fermion respectively. I will use the bases to study small deformations of the two theories. Assuming no new operators appear in the OPE, the generalized free fermion allows no small deformation, and the generalized free boson allows a one-parameter deformation, which coincides with the AdS_2 four-point contact interaction at the leading order. Time allowing, I will discuss the connection of this work to the conformal bootstrap a la Polyakov.

We consider planar hairy black holes in five dimensions with a real scalar field in the Breitenlohner-Freedman window and show that is possible to derive a universal formula for the holographic speed of sound for any mixed boundary conditions of the scalar field. As an example, we locally construct the most general class of planar black holes coupled to a single scalar field in the consistent truncation of type IIB supergravity that preserves the SO(3)xSO(3) R-symmetry group of the gauge theory. We obtain the speed of sound for different values of the vacuum expectation value of a single trace operator when a double trace deformation is induced in the dual gauge theory. In this particular family of solutions, we find that the speed of sound exceeds the conformal value. Finally, we generalize the formula of the speed of sound to arbitrary dimensional scalar-metric theories whose parameters lie within the Breitenlohner-Freedman window

I will discuss constraints on the S-matrix of gapped, Lorentz invariant quantum field theories due to crossing symmetry, analyticity and unitarity.  In particular I will bound cubic couplings, quartic couplings and scattering lengths relevant for the elastic scattering amplitude of two identical scalar particles. After a warm-up in 1+1 dimensions I will move to 3+1 dimensions.  In the cases where the results can be compared with results in the older S-matrix literature they are in excellent agreement.

We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs). In large N CFTs with a large gap to single-trace higher spin operators, we show that the coupling of two stress tensors to other single-trace operators ("TTO") is suppressed by powers of the higher spin gap, dual to the mass scale of higher spin particles in AdS. The absence of light higher spin particles is thus a necessary condition for the existence of a consistent truncation to general relativity in AdS. We are led to propose that, in general, the inverse gap scale is the CFT "dual" of an AdS derivative in a classical action. These results are derived by imposing unitarity on mixed systems of spinning four-point functions in the Regge limit. Using the same method, but without imposing a large gap, we derive new inequalities on TTO-type couplings valid in any CFT.

Many researchers have been studying the time evolution of entanglement entropy in the sudden quenches where a characteristic mass scale suddenly changes. It is well-know that in these quenches, the change of entanglement entropy become thermal entropy which is proportional to a subsystem size in the late time. However, we do not know which quenches thermalize a subsystem. In our works, we have been studied the time evolution of quantum entanglement in the global quenches with finite quench rate (smooth quenches). Thus, we found that diabaticity plays an important role, so that quenches thermalize the subsystem.

Gravitational shockwaves may signal the breakdown of effective field theory near black hole horizons. Motivated by this, I will revisit the Dray-‘t Hooft solution and explain how to generalize it to the Kerr-Newman background. In doing so I will emphasize the method of spin coefficients (the Newman-Penrose formalism) in its compacted form (the Geroch-Held-Penrose formalism).