Scattering data can be generically described in terms of monodromies. Here we obtain scattering amplitudes for conformally coupled scalar fields Kerr-de Sitter black holes using this monodromy technique. The only non-trivial parameter, the composite parameter $\sigma_{ij}$ between two regular singular points, solved implicitily Painlev\'e VI $\tau$-function. application Virasoro conformal blocks to solve latter now interpreted as a verification striking relationship symmetry and holes.

Quasinormal modes are characteristic oscillatory that control the relaxation of a perturbed physical system back to its equilibrium state. In this work, we calculate QNM frequencies and angular eigenvalues Kerr--de Sitter black holes using novel method based on conformal field theory. The spin-field perturbation equations background spacetime essentially reduce two Heun's equations, one for radial part part. We use accessory parameter expansion equation, obtained via isomonodromic...

We study the scattering of a massless scalar field in generic Kerr background. Using particular gauge choice based on current conservation radial equation, we give formula for coefficient terms composite monodromy parameter σ between inner and outer horizons. isomonodromy flow, calculate exactly Painlevé V τ -function. also show that eigenvalue problem angular equation (spheroidal harmonics) can be calculated using same techniques. use recent developments relating -function to Liouville...

We apply the method of isomonodromy to study scattering a generic Kerr-NUT-(A)dS black hole. For values charges, problem is related connection Painlevé VI transcendent. review few facts about VI, Garnier systems and Hamiltonian structure flat connections in Riemann sphere. then outline for computing amplitudes based on Hamilton-Jacobi Painlevé, discuss implications result hole complementarity.

Non-relativistic field theories with anisotropic scale invariance in (1+1)-d are typically characterized by a dispersion relation $E\sim k^{z}$ and dynamical exponent $z>1$. The asymptotic growth of the number states these can be described an extension Cardy formula that depends on $z$. We show this result recovered counting partitions integer into $z$-th powers, as proposed Hardy Ramanujan century ago. This gives novel relationship between characteristic energy cylinder radius ground state...

A bstract Classical conformal blocks appear in the large central charge limit of 2D Virasoro blocks. In AdS 3 / CFT 2 correspondence, they are related to classical bulk actions and used calculate entanglement entropy geodesic lengths. this work, we discuss identification Painlevé VI action showing how isomonodromic deformations naturally context. We recover accessory parameter expansion Heun’s equation from τ -function. also c = 1 -function leads a novel approach 4-point block.

A bstract We compute an upper bound on the circuit complexity of quantum states in 3 d Chern-Simons theory corresponding to certain classes knots. Specifically, we deal with torus Hilbert space that are knot complements 3-sphere arbitrary These can be constructed from unknot state by using representation S and T modular transformations as fundamental gates. The is saturated semiclassical limit theory. results then generalized for a family multi-component links obtained “Hopf-linking”...

Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in field theories. In 3D Chern-Simons theory, these can be found crossing braiding matrices four-point conformal blocks boundary 2D CFT. We calculate for $W_N$ with one component fundamental representation another a rectangular $SU(N)$, which used to obtain HOMFLY knot cases. also discuss how our approach generalized higher-representations algebra.

We summarize recent results by the authors [7, 8, 35] on extraction of scattering amplitudes for scalar fields in Kerr/Kerr-de Sitter backgrounds. Analytical, closed forms are found terms Painlevé V and VI transcendents generic values physical parameters.

The Generalized Gibbs Ensemble (GGE) is relevant to understand the thermalization of quantum systems with an infinite set conserved charges. In this work, we analyze GGE partition function 2D Conformal Field Theories (CFTs) a U(1) charge and Benjamin-Ono$_{2}$ (qBO$_{2}$) hierarchy We use Alday-Gaiotto-Tachikawa (AGT) correspondence express thermal trace in terms Alba-Fateev-Litvinov-Tarnopolskiy (AFLT) basis descendants, which diagonalizes all thermodynamic semiclassical limit, including...

We propose the holographic principle as a dynamical cutoff for any quantum theory of gravity with geometric description at low energies, incorporating ideas effective field theory. illustrate proposal by revisiting problem defining measure homogeneous and isotropic spacetimes coupled to scalar conclude discussing implications inflationary model.