Quantum Fields and Strings

In this talk we combine integrability and conformal bootstrap to learn about correlation functions of planar maximally supersymmetric Yang- Mills theory. Focusing on correlators of four stress-tensor multiplets, we first introduce a set of dispersive sum rules that are only sensitive to single-traces in the OPE expansion (this is advantageous because this data is available from integrability). We then construct combinations of the sum rules which determine one-loop correlators. Further, we discuss how to employ the sum rules in numerical bootstrap to nonperturbatively bound planar OPE coefficients. As an example, we show a nontrivial upper bound on the OPE coefficient of the Konishi operator outside the perturbative regime. 

The AdS/CFT correspondence is one of the most important breakthroughs of the last decades in theoretical physics. A recently proposed way to get insights on various features of this duality is achieved by discretizing the Anti-de Sitter spacetime. Within this program, we consider the Poincaré disk and we discretize it by introducing a regular hyperbolic tiling on it. The features of this discretization are expected to be identified in the quantum theory living on the boundary of the hyperbolic tiling. In this talk, we discuss how a class of boundary Hamiltonians can be naturally obtained in this discrete geometry via an inflation rule that allows constructing the tiling using concentric layers of tiles. The models in this class are aperiodic spin chains. Using strong-disorder renormalization group techniques, we study the entanglement entropy of these boundary theories, identifying a logarithmic growth in the subsystem size, with a coefficient depending on the bulk discretization parameters.

Zoom link:  https://pitp.zoom.us/j/95849965965?pwd=eEx5Q0gxR2orR0dzS2pQbG8rR09oUT09

The fact black holes carry statistical entropy proportional to their horizon area implies that quantum information concepts are geometrized in gravity. This idea obtains a particular manifestation in the AdS/CFT correspondence, where it is believed that the quantum information content in the dual field theory state can be used to reconstruct the bulk space-time geometry. The calculation of entanglement entropy from geodesics in the bulk space-time have clarified this idea to some extend.

In this talk, I will consider two aspects of quantum information theory in relation to holography: First, I will discuss a refinement of entanglement entropy for systems with conserved charges, the so-called symmetry resolved entanglement. It measures the entanglement in a sector of fixed charge. I will present how to calculate the symmetry-resolved entanglement entanglement in two-dimensional conformal field theories with Kac-Moody symmetry, and also within W_3 higher spin theory. I will also discuss the geometric realization in the dual AdS space-time, and how the independent calculation there leads to a new test of the AdS3/CFT2 correspondence.

Second, I will discuss the large N limit of Nielsen's operator complexity on the SU(N) manifold, with a particular choice of cost function based on the Laplacian on the Lie algebra, which leads to polynomial (instead of exponential) penalty factors. I will first present numerical results that hint to the existence of chaotic and hence ergodic geodesic motion on the group manifold, as well show the existence of conjugate points. I will then discuss a mapping between the Euler-Arnold equation which governs the geodesic evolution, to the Euler equation of two-dimensional idea hydrodynamics, in the strict large N limit.

Within the AdS/CFT correspondence, the entanglement properties of the CFT are related to wormholes in the dual gravity theory. This gives rise to questions about the factorisation properties of the Hilbert spaces on both sides of the correspondence.  We  show how the Berry phase, a geometrical phase encoding information about topology, may be used to reveal the Hilbert space structure. Wormholes are characterized by a non-exact symplectic form that gives rise to the Berry phase. For wormholes connecting two spacelike regions in AdS3 spacetimes, we find that the non-exactness is linked to a variable appearing in the phase space of the boundary CFTs. Mathematical concepts such as coadjoint orbits and geometric actions play an important role in this analysis.  We classify Berry phases according to the type of dual bulk diffeomorphism involved, distinguishing between Virasoro, gauge and modular Berry phases.

In addition to its relevance for quantum gravity, the approach presented also suggests how to experimentally realize the Berry phase and its relation to entanglement in table-top experiments involving photons or electrons. This provides a new example for relations between very different branches of physics that follow from the AdS/CFT correspondence and its generalizations. Based on 2202.11717 and 2109.06190.

Zoom link: https://pitp.zoom.us/j/96113910200?pwd=YXJnSWxiMHRIb21xdGFnNFM0cFFvUT09

The 6d N = (2,0) theories are superconformal field theories believed to describe the low-energy dynamics of N coincident M5-branes. These theories don't have a known lagrangian description and remain largely mysterious, so it is an interesting question how one might calculate observables there.  An exciting prospect is to use the analytical conformal bootstrap, which offers a way to systematically calculate 1/N corrections at large N. In this talk I will present the bootstrap approach to a case study, that of calculating the 2-point function of stress tensors in the presence of a surface defect.  This setup turns out to be remarkably simple and helps us address some technical issues faced in similar calculations, notably we can derive a supersymmetric inversion formula and check crossing symmetry explicitly. I will also comment on the interpretation of our result in the context of holography, of the chiral algebra construction of Beem et al. and on what it can reveal about the interactions between M2 and M5-branes.

Zoom link:  https://pitp.zoom.us/j/92631930165?pwd=Qm9MQzlNdHo0WGJINUZBUVNaOXZxZz09

We present a new class of supersymmetric localization principles in the context of supersymmetric quantum mechanics. Contrary to the standard localization, this new principle deals with non-supersymmetric observables. We apply this to provide a path integral understanding of trace formulas in mathematics. Our examples will contain both integrable and chaotic quantum systems, namely trace formulas on compact Lie groups by Eskin, and generic locally symmetric space by Selberg. 

Zoom Link:  https://pitp.zoom.us/j/99332291865?pwd=c0kyUUlWN1AxeXpvNmRkNHRSRXNXdz09

In this talk, I will begin with a brief introduction to celestial holography and setting up the celestial amplitudes, before diving into some recent results on examining the BCFW recursion relations for celestial amplitudes. We start by recasting the celestial incarnation of the BCFW shift as a generalization of the action of familiar asymptotic symmetries on hard particles, before focusing on two limits: large-z and infinitesimal-z. We then discuss how the celestial CFT data encodes the large-z behavior determining which shifts are allowed, while the infinitesimal limit is tied to the celestial bootstrap program via the BG equations that constrain the MHV sector.

Zoom link: https://pitp.zoom.us/j/99231185135?pwd=OWk4S2ZITmFGSmVsQUwwbHI5NW1rUT09

The search for pragmatic observables of quantum gravity remains at the forefront of fundamental physics research. A large set of ideas collectively known as the gauge-gravity duality have proven fruitful in tackling this problem. While such a duality is believed to universally govern gravitational theories, its nature in theories of gravity that describe our universe to a good degree of approximation is still little understood.

In this talk I will discuss efforts in formulating a holographic correspondence for gravity in four-dimensional asymptotically flat spacetimes. The proposed dual theory lives on a two-dimensional celestial sphere at infinity and is constrained by a wide range of symmetries. I present recent evidence for this proposal by showing that it arises naturally in a flat space limit of AdS/CFT. I will illustrate this construction with two related examples: the propagation of a particle in a shockwave background and the high-energy scattering of 2 particles.

Zoom Link: https://pitp.zoom.us/j/97426266597?pwd=UmhncFR6NExFVzI2SlJwdE1LeUlIQT09

A black hole quantum state (Hartle-Hawking or Boulware)  is usually defined in a fixed background of a classical black hole. In my talk I will discuss the corresponding space-time geometry when the back-reaction is taken into account. The important questions include: does the back-reacted geometry always contain a horizon?; how it depends on the choice of the quantum state?;  and what is the right choice for the quantum state for the non-physical fields such as ghosts? I will answer these and other questions in the context of a two-dimensional dilaton gravity. The talk is based on a joint recent work with D. Sarkar and Y. Potaux, arXiv:2112.03855.

Zoom Link: https://pitp.zoom.us/j/5053597405?pwd=YjU2VVF1L3A1dmR1VWpPMHZFQW9rdz09

Three dimensional conformal field theories(CFTs) describe important critical physics in the real world. In the past few years much progress has been made in 3D CFTs using the conformal bootstrap. In particular, using numerical bootstrap, the critical exponents of the 3D Ising, Super-Ising, O(2), O(3) CFTs have been determined precisely with rigorous error bars, while using analytic bootstrap, the information of the leading twist operators at large spins can be computed analytically. The two bootstrap approaches are sensitive to different regions of the spectrum and complement each other. In this talk, I will first give a general review of the numerical bootstrap and analytic bootstrap. Then I will discuss how to combine the numerical bootstrap with the analytic lightcone bootstrap, i.e. a hybrid bootstrap method. As a result, the bootstrap prediction for the actual CFT can be significantly improved.

Zoom Link: https://pitp.zoom.us/j/94186668943?pwd=ejRRb0M4VXNjeVVCWGdnTHQyaWRyQT09

There are two different standard ways of endowing a physical theory with a symplectic structure: the canonical and the covariant. The former is derived from the well-known symplectic structure of a certain cotangent bundle. The latter is based on the variational calculus. Including a boundary in the canonical formalism poses no problem, however, in the covariant formalism things break apart. In this talk, I will briefly introduce both formalisms without boundary and explain in detail a new framework that allows us to include boundaries in a straightforward way. To show it in action, time permitting, I will apply it to several theories of gravity. Finally, I will briefly show a new result where we proved that, actually, the canonical and covariant formalisms are equivalent in full generality.

Zoom Link: https://pitp.zoom.us/j/97641588140?pwd=dFl0SFdHOG5BYko2djNVWk11UkhSUT09

Holographic complexity proposals are interesting because, on one hand, they express universal properties of black hole interiors and, on the other, they go beyond the area-centric view on quantum gravity. Our best take on complexity in quantum field theory is based on assigning a cost to circuits generated by time-dependent Hamiltonians and its minimization. I will discuss recent progress on understanding how the relevant circuits are realized in holography and what are possible gravity duals to good costs. Based on 2112.12158, 2203.08842 and work in progress.

Zoom Link: https://pitp.zoom.us/j/96487059058?pwd=ZHk1ZHpXMEZoT0UycUZqTEdIb1ZpQT09