# Anatoly Dymarsky

My research is on theoretical high-energy physics. I study quantum field theory with the goal of understanding universal principles constraining non-pertubative dynamics. Some of my research on applied mathematics is described here.

**Relation between scale and conformal invariance**

It has been known for several decades that scale invariance in unitary QFTs is "automatically" enhancing to full conformal symmetry. Despite recent progress in four space-time dimensions linking this symmetry enhancment to irreversibility of the RG flow, the underlying mechanism relating scale and conformal symmetries is still poorly understood. In my research I aim to develop a better understanding of the relation between scalae and conformal invariance and link it to the properties of entanglement entropy, which is known to encode irreversibility of RG flow in three dimensions.

**Conformal bootstrap for operators with spin **

Numerical conformal bootstrap is a powerful new approach to study both the landscapce of conformal theories and certain particular models. One promising direction is to apply bootstrap to operators with spin, such as conserved currents, stress-energy tensor and higher-spin fields. In my research I utilize available symmetries, such as consevation constraints, to remove potential degeneracies and simply formulation of the boostrap equations.

**Emergence of statistical thermodynamics from quantum mechanics**

Emergence of statistical mechanics from unitary evolution of an isolated quantum system is an active research topic with many interesting questions remain open. A significant progress was made understanding thermalization of "chaotic" isolated systems in terms of Eigenstate Thermalization Hypothesis (ETH). In my research I study potential extentions and generalizations of this approach in case of models with local interactions, both lattice and field-theoreticl. In the discrete case I heavily rely on numerical methods akin to direct diagonalization and supercomputing facilities. In the continous case the employed methods are originating from qunatum information theory and holography.