Quantum Fields and Strings

I will describe 4pt conformal blocks for scalar operators in diverse dimensions by using a single unified formalism, and explain a property of the conformal blocks known as stability. This stability implies that when writing conformal blocks as certain multivariate series, the coefficients of this expansion only depend on Young diagrams. In particular, we can bosonise the conformal computation and simply focus on compact groups. In this framework the blocks are polynomials of the BC root system after we apply complementation. I will then explain the connection with mathematics and show how to formulate a superconformal Cauchy identity which yields the CPW of any free theory diagram in any dimension. For discussion, I will finally mention q-deformations results.

Zoom Link: https://pitp.zoom.us/j/96912692269?pwd=TE8vT01mam9lQjhVV3VSYUtWR2d5Zz09

In this talk, I will discuss the duality between the two-dimensional type 0B string theory and its dual matrix quantum mechanics. This duality has been a source of motivation and a useful toy model to explore many new features of string theory. I will first revisit the computation of closed string scattering amplitudes in string perturbation theory, using new numerical methods to compute Virasoro conformal blocks in 2d supersymmetric conformal field theories. Then, I will describe a worldsheet formalism to include non-perturbative corrections to closed string scattering amplitudes, mediated by D-instantons. This formalism is of general applicability, and can be straightforwardly implemented in other string models. In the type 0B string theory, this will allow us to extend the duality dictionary beyond perturbation theory.

In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermofield double state. We provide explicit constructions in the boundary theory of infalling time evolutions which can take bulk observers behind the horizon. The constructions also help to illuminate the boundary emergence of the black hole horizons, the interiors, and the associated causal structure. A key element is the emergence, in the large N limit of the boundary theory, of a type III1 von Neumann algebraic structure and the half-sided modular translation structure associated with it.

Zoom Link: https://pitp.zoom.us/j/99458239757?pwd=YTBRdXdwTjltMkdZc0Q4WW1jQjA3QT09

I will describe an approach to extracting the physical consequences of S-duality of four-dimensional N = 4 super Yang-Mills (SYM) and its string theory dual based on SL(2,Z) spectral theory. I will show that processing S-duality in this way leads to strong consequences for the CFT data, both perturbatively and non-perturbatively in all parameters. In large-N limits, I will argue for the existence and scaling of non-perturbative effects, both at large N and at strong 't Hooft coupling. An elegant benchmark for these techniques is a certain integrated stress-tensor multiplet four-point function, whose form I will elucidate. I will explain how the ensemble average of CFT observables over the N = 4 supersymmetric conformal manifold with respect to the Zamolodchikov measure is cleanly isolated by the spectral decomposition, and will show that the large-N limit of the ensemble average is equal to the strong-coupling limit of the observable in the planar theory, which is its value in type IIB supergravity on AdS_5 x S^5. This embeds an emergent averaged holographic duality within the conventional holographic paradigm.

Zoom link:  https://pitp.zoom.us/j/95197874062?pwd=QU4vbXNNeFVmS0hNbTVLL24wdDBndz09

Zoom link:  https://pitp.zoom.us/j/96132106700?pwd=L3ZMOXltZks4Y25abUl5TTdhZTVKUT09

Since the advent of holography, a lot of progress has been made in our understanding of quantum gravity in AdS. However less is known of its flat space counterpart, even though quantum gravity was certainly first formulated in flat space. Various programs have emerged since, like Celestial Holography or Carrollian Holography, both formulated in four and higher dimensions which is the closest to reality but makes the computation of highly quantum quantities difficult. I will present a 2d model of flat space gravity in which these difficulties can be tackled. This model is dubbed the "Cangemi — Jackiw model" after the authors of arXiv:9203056. It is a model of flat space gravity that can be reformulated in terms of a boundary action whose solutions are Rindler patches. I will explain how this “boundary graviton” reformulation gives access to fully quantum Euclidean results. In particular we will compute the exact spectrum of the Bondi Hamiltonian and show that it can be non-perturbatively completed by a matrix model. I will also comment on scrambling in flat space.

Based on “From black holes to baby universes in CGHS gravity” with Victor Godet (https://arxiv.org/abs/2103.13422) and an upcoming paper with Arjun Kar, Lampros Lamprou and Felipe Rosso.

Zoom Link: https://pitp.zoom.us/j/95709808325?pwd=QVdFUFZiTHVvMWlDb211U3kxQ0ZkZz09

In this talk I will consider massless scattering from the point of view of the position, momentum, and celestial bases with a view to advancing a holographic principle for asymptotically flat spacetimes. Within the soft sector, these different languages highlight distinct aspects of the 'infrared triangle': quantum field theory soft theorems arise in the limit of vanishing energy, memory effects are described via shifts of fields along retarded time, and celestial symmetry algebras are realized via currents that appear at special values of the conformal dimension. The latter are determined by the global conformal multiplets in celestial CFT referred to as 'celestial diamonds'. These diamonds degenerate beyond the leading universal soft modes and the standard interpretation of the infrared triangle breaks down: we have neither an obvious asymptotic symmetry nor a Goldstone mode but we do have a soft theorem, and hence a version of a memory effect. I will discuss various aspects of celestial CFT surrounding these Goldstone-like, or Goldilocks, modes and their canonically paired memory modes. They play an important role in constraining celestial OPEs and for understanding the interpretation and implications of the (semi-)infinite tower of tree-level symmetry currents which may pose powerful constraints on consistent low energy effective field theories.

Zoom Link: https://pitp.zoom.us/j/95785822777?pwd=cVJWYVJBS1E3aDJPT1ZSTmlZbzVQQT09

Euclidean wormholes are exotic types of gravitational solutions that we still don't understand completely. In the first part of the talk, I will analyze asymptotically AdS wormhole solutions from a gravitational point of view. By studying correlation functions of local and non-local operators, the universal properties that any putative holographic dual should exhibit, become manifest. In the second part, I will describe some concrete field theoretic models (both effective and microscopic) that share these properties.

TTbar and JTbar - deformed CFTs provide an interesting example of non-local, yet UV-complete two-dimensional QFTs that are entirely solvable. I will start by showing that both classes of theories possess Virasoro x Virasoro or Virasoro- Kac- Moody x Virasoro - Kac- Moody symmetry. For the case of JTbar, I will discuss the classical realization of these symmetries in terms of field-dependent coordinate transformations and show how the associated generators can be used to define an analogue of "primary" operators in this non-local theory, whose correlation functions are entirely fixed in terms of those of the undeformed CFT. In particular, two and three-point functions are simply given by the corresponding momentum-space correlator in the undeformed CFT, with all dimensions replaced by particular momentum-dependent conformal dimensions. Interestingly, scattering amplitudes off the near-horizon of extremal black holes are known to take a strikingly similar form.

Several puzzles and issues in quantum gravity are related to the question of what type of high-energy information is actually available to low-energy observers. In this talk I will try to argue that the best description available to a low-energy observer is probably of a statistical nature. Such a statistical description naturally connects to e.g. the eigenstate thermalization hypothesis, and wormholes and the apparent lack of factorization. I will describe this statistical picture and the evidence we have for it, and what we could possibly learn from it. Partially based on work in progress.

Zoom Link: https://pitp.zoom.us/j/96646337719?pwd=UVRKN3Y4Q05xNXk1VExOenYwSFZvZz09

In this talk, we will discuss the late time behavior of out of time ordered correlators (OTOC). First part of the talk, we argue the nonlinear behavior of OTOC for general chaotic system is controlled by a Dray t’Hooft like action. Second part of the talk, we will discuss the late time nonperturbative effects in OTOC and its relation with random unitary behavior.

A salient feature of black holes near extremality is the appearance of an AdS$_2$ throat in their near-horizon geometry. Depending on the underlying theory, these AdS$_2$ throats may be unstable to fragmentation, wherein a single throat is instead replaced by a tree-like structure of branched AdS$_2$ throats. For Einstein-Maxwell theory, the underlying reason behind this instability is the existence of multi-centered configuration in the moduli space of black hole solutions at fixed total charge. Given the success of the Schwarzian/SYK paradigm for understanding a single AdS$_2$ it is time to revisit the fragmentation story. To build up intuition, I will present a model, studied in the statistical mechanics literature, that shares many features with SYK, including exact solvability at large-N and an emergent conformal symmetry that gets weakly broken in the UV. The novel feature of this model is the appearance of a spin glass phase at O(1) temperatures, which I will try to relate to the fragmentation story.