Related papers: Circuit Complexity for Carrollian Conformal (BMS) …
In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic…
According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the…
We investigate quantum field theories in two dimensions (2d) with an underlying Bondi-van der Burgh-Metzner-Sachs (BMS) symmetry augmented by $\mathfrak{u}(1)$ currents. These field theories are expected to holographically capture features…
We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS$_{3}$ algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis…
We rewrite the Chern-Simons description of pure gravity on global AdS$_3$ and on Euclidean BTZ black holes as a quantum field theory on the AdS boundary. The resulting theory is (two copies of) the path integral quantization of a certain…
Conformal Carrollian groups are known to be isomorphic to Bondi-Metzner-Sachs (BMS) groups that arise as the asymptotic symmetries at the null boundary of Minkowski spacetime. The Carrollian algebra is obtained from the Poincare algebra by…
This thesis focuses on two research areas: non-relativistic field theories and complexity. In the first part we review the general classification of the trace anomaly for 2+1 dimensional field theories coupled to a Newton-Cartan background…
The BMS (Bondi-van der Burg-Metzner-Sachs) symmetry arises as the asymptotic symmetry of flat spacetime at null infinity. In particular, the BMS algebra for three dimensional flat spacetime (BMS$_3$) is generated by the super-rotation…
We define and study asymptotic Killing and conformal Killing vectors in $d$-dimensional Minkowski, (A)dS, $\mathbb{R}\times S^{d-1}$ and ${\rm AdS}_2\times S^{d-2}$. We construct the associated quantum charges for an arbitrary CFT and show…
Conformal Carroll symmetry generically arises on null manifolds and is important for holography of asymptotically flat spacetimes, generic black hole horizons and tensionless strings. In this paper, we focus on two dimensional (2d) null…
Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a…
Three dimensional wormholes are global solutions of Einstein-Hilbert action. These space-times which are quotients of a part of global AdS$_{3}$ have multiple asymptotic regions, each with conformal boundary $S^{1}\times\mathbb{R}$, and…
The crossing equations of a conformal field theory can be systematically truncated to a finite, closed system of polynomial equations. In certain cases, solutions of the truncated equations place strict bounds on the space of all unitary…
We discuss c-functions and their holographic counterpart for two-dimensional field theories with Carrollian conformal fixed points in the UV and the IR. Specifically, we construct asymptotically flat domain wall solutions of…
Conformal invariance often accompanies criticality in Hermitian systems. However, its fate in non-Hermitian settings is less clear, especially near exceptional points where the Hamiltonian becomes non-diagonalizable. Here we investigate…
We calculate Nielsen's circuit complexity of coherent spin state operators. An expression for the complexity is obtained by using the small angle approximation of the Euler angle parametrisation of a general $SO(3)$ rotation. This is then…
We systematically study inhomogeneous Hamiltonians in two-dimensional conformal field theories within the framework of the AdS/CFT correspondence by relating them to two-dimensional curved backgrounds. We propose a classification of…
Surface-charge algebra associated with BMS$_4$ symmetry on the null infinity of asymptotically flat spacetime is studied via the Hamiltonian framework. A coordinate system, where boundaries of constant-time hypersurfaces cross the null…
In IIB string theory on AdS$_3$ background with NS-NS fluxes, we show that Brown-Henneaux asymptotic Killing vectors can be derived by requiring both the worldsheet equations of motion and Virasoro constraints are preserved near the…
We elaborate on the proposal of flat holography in which four-dimensional physics is encoded in two-dimensional celestial conformal field theory (CCFT). The symmetry underlying CCFT is the extended BMS symmetry of (asymptotically) flat…