2d Integrable field theories from 4d CS theory with 2d systems and its lattice discretization
The 4d Chern-Simons (CS) theory proposed by Costello,Yamazaki and Witten is proposed as a framework that allows a systematic description not only of (1+1)-d integrable lattice models, but also of 2d classical integrable field theories. This would allow for a unified description of the relationship between integrable lattice models and field theories in terms of a single gauge theory. In this talk, as a first step towards understanding this relation, I derive the Faddeev-Reshetikhin (FR) model, which can be discretised preserving the quantum integrability, from a 4d CS theory coupled with 2d free field theories. The derivation is based on my work [2012.07370] with K.Yoshida and O.Fukushima in Kyoto university.
Then, I give a rough sketch of the lattice discretisation of the FR model in the context of 4d CS theory. This is achieved by discretising the 2d theory coupled to the 4d CS theory into Wilson lines, which would provide a framework for studying the lattice discretisation of 2d integrable field theories. The work on this discretisation is in progress with M.Yamazaki and M.Ashwinkumar in IPMU.
the 27th of September 2022, 14:30
The spin 1/2 lurking in the Rarita-Schwinger system
The Rarita-Schwinger (RS) field belongs to a reducible representation of the Lorentz group containing spin-3/2 and spin-1/2 irreps. The Dirac Hamiltonian analysis shows that the dynamical degrees of freedom of the RS system depends crucially on whether the so-called Dirac Conjecture is assumed or not. In the affirmative case, only the spin-3/2 propagates, but the Lagrangian and the Hamiltonian equations are not equivalent; in the opposite case, the Lagrangian and Hamiltonian forms are equivalent and both s=1/2 and s=3/2 propagate. Both points of view are tenable and consistent, but describe different physical systems.
the 20th of September 2022, 14:30
Fluid dynamical interpretation of the Einstein-Cartan field equations with respect to a generic null hypersurface
In the present work, we study the dynamics of a general null
hypersurface in the Einstein Cartan (EC) theory generated by a null
vector field $l^a$. We see that under a particular relation between the
torsion tensor and the null generators called the geodesic constraint,
the dynamical evolution of the Hajicek one-form is governed by the
component $G_{ab} l^a q_c^b$, where $g_{ab}$ is the induced metric on an
orthogonal spacelike cross-section of the null surface and $G_{ab}$ is the
analogue of the Einstein tensor in spacetime with intrinsic torsion.
Using the gravitational field equations for the EC theory, we see that
above mentioned evolution equations can be provided a fluid-dynamical
interpretation respectively. The relevant thermodynamic and fluid
parameters have been properly identified. The dynamics of the Hajicek
one-form has been studied in a local inertial frame and its
correspondence with Cosserat fluid has been established.
the 13th of September 2022, 16:00
Gravitational Physics and Scattering Amplitudes
Scattering amplitudes have recently found a new application to classical gravitational-wave physics. In this talk I will discuss why amplitudes can be useful in this area, and outline how to extract classical observables from the amplitudes. We will see that the basic aspects of classical physics in turn yields interesting new constraints on the structure of multiloop, multileg amplitudes.
the 7th of June 2022, 14:30
Gluon scattering in AdS from CFT
I will present a class of holographic correlators between half-BPS operators in a vast array of SCFTs with non-maximal superconformal symmetry in dimensions d=3,4,5,6. Via AdS/CFT, these four-point functions are dual to gluon scattering amplitudes in AdS. Exploiting the notion of MRV limit I will show that, at tree level, all such correlators are completely fixed by symmetries and consistency conditions. Our results encode a wealth of novel CFT data and exhibit various emergent structures, including Parisi-Sourlas supersymmetry, hidden conformal symmetry and color-kinematics duality in AdS. The talk will be based on https://arxiv.org/pdf/2103.15830.pdf.
the 6th of June 2022, 14:30
7d SYM, negative coupling and instantons
Being non-renormalizable, SYM theories in d>4 are not well-defined by themselves and need non-trivial UV-completions. Using supersymmetric localization, one can obtain a glimpse into the structure of these UV completions. Focusing on the 7d SYM, we show that there is a regime where the effective coupling becomes negative. The theory has instanton branes which contribute to the partition function non-trivially. Remarkably, the full partition functions stays well defined even for negative coupling. Our results imply that the UV completion has two distinct weakly coupled regimes, one of which is described by a supersymmetry multiplet with a three-form field.
the 31st of May 2022, 14:30
Cobordism and K-theory: tadpoles and end-of-the-world branes
The absence of global symmetries is widely believed to be a fact in quantum gravity. Recently, this has been generalised to the statement that the cobordism group of quantum gravity must be trivial. Indeed, a non-trivial group detects a (higher-form) global symmetry, which has then to be either gauged or broken. In the case in which it is gauged, I will show that there is a non-trivial interplay between cobordism and K-theory, leading to the construction of string theory tadpoles from a bottom-up perspective. In the case in which the cobordism symmetry is broken, defects have to be introduced into the setup. I will give evidence for the possible presence of a new 7-brane object in string theory, which should be needed to break a cobordism symmetry in the T-dual version of the USp(32) type I string.
the 17rd of May 2022, 14:30
From dS to AdS, and back
In the search for a complete description of quantum mechanical and gravitational phenomena, we are inevitably led to consider observables on boundaries at infinity. This is the common mantra that there are no local observables in quantum gravity and gives rise to the tantalising possibility of a purely boundary--or holographic--description of physics in the interior. The AdS/CFT correspondence provides an important working example of these ideas, where the boundary description of quantum gravity in anti-de Sitter (AdS) space is an ordinary quantum mechanical system-- in particular, a Lorentzian Conformal Field Theory (CFT)--where the rules of the game are well understood. It would be desirable to have a similar level of understanding for the universe we actually live in. In this talk I will explain some recent efforts that aim to understand the rules of the game for observables on the future boundary of de Sitter (dS) space. Unlike in AdS, the boundaries of dS space are purely spatial with no standard notion of locality and time. This obscures how the boundary observables capture a consistent picture of unitary time evolution in the interior of dS space. I will explain how, despite this difference, the structural similarities between dS and AdS spaces allow to forge relations between boundary correlators in these two space-times. These can be used to import techniques, results and understanding from AdS to dS.
the 3rd of March 2022, 14:30
Big-Bang type singularities in QFT and string theory on time-dependent orbifolds
Time-dependent orbifolds generated from Minkowski spacetime are very useful toy models to address the study of Big-Bang type singularities. After introducing their geometry, I will review some of the results presented in the literature when they have been considered as cosmological backgrounds of string theory. I will in particular discuss the most serious issue that has been encountered: the unusual divergences found in the computation of some tree-level string scattering amplitudes. I will then move to the study of an effective quantum field theory on these models, which shows where the real nature of their pathological behavior lies. Finally, in order to cure the divergences, I will introduce a noncommutative framework which seems promising both from the QFT and the string theory point of view.
the 12th of April 2022, 14:00
I will discuss the Cardy-like limit of the superconformal index of generic N=1 SCFTs with ABCD gauge algebra, providing strong evidence for a universal formula that captures the behavior of the index at finite order in the rank and in the fugacities associated to angular momenta. The formula extends previous results valid at lowest order, and generalizes them to generic SCFTs. The validity of our proposal can be corroborated by studying several examples, beyond the well-understood toric class. The index can also be computed for models without a weakly-coupled gravity dual, whose gravitational anomaly is not of order one.
the 5th of April 2022, 14:30