Search Talks

This is a joint work with A.Kuznetsov and L.Rybnikov.

We study a moduli problem on a nodal curve of arithmetic genus 1, whose solution is an open subscheme in the zastava space for projective line. This moduli space is equipped with a natural Poisson structure, and we compute it in a natural coordinate system. We compare this Poisson structure with the trigonometric Poisson structure on the transversal slices in an affine flag variety.

We conjecture that certain generalized minors give rise to a cluster structure on the trigonometric zastava.

The structure of entanglement can yield new physical insights into strongly interacting quantum critical states. I’ll describe key properties of the entanglement entropy of conformal field theories (CFTs) in 2+1d. In particular, we’ll see that sharp corners in the entangling surface contribute a regulator-independent function that depends non-trivially on the corner angle. I’ll argue that in the smooth limit this function yields the 2-point function of the stress tensor. This sheds light on recent cutting edge simulations of the quantum critical Ising, XY and Heisenberg models. I’ll also present a new lower bound for this function. I will then generalize to Rényi entropies, which yields a simple procedure to extract the thermal entropy using corner entanglement of the groundstate alone. Connections will be made to CFTs in 1+1d and 3+1d, as well as to Lifshitz theories.

I distinguish two types of reduction within the context of quantum-classical relations, which I designate “formal” and “empirical”. Formal reduction holds or fails to hold solely by virtue of the mathematical relationship between two theories; it is therefore a two-place, a priori relation between theories. Empirical reduction requires one theory to encompass the range of physical behaviors that are well-modeled in another theory; in a certain sense, it is a three-place, a posteriori relation connecting the theories and the domain of physical reality that both serve to describe. Focusing on the relationship between classical and quantum mechanics, I argue that while certain formal results concerning singular ℏ→0 limits have been taken to preclude the possibility of reduction between these theories, such results at most provide support for the claim that singular limits block reduction in the formal sense; little if any reason has been given for thinking that they block reduction in the empirical sense. I then briefly outline a strategy for empirical reduction that is suggested by work on decoherence theory, arguing that this sort of account remains a fully viable route to the empirical reduction of classical to quantum mechanics and is unaffected by such singular limits.

In effective field theory, causality fixes the signs of certain interactions.  I will describe how these Lorentzian constraints are encoded in the Euclidean theory, and use the conformal bootstrap to derive analogous causality constraints in CFT. Applied to spinning fields, these constraints include (some of) the Hofman-Maldacena bounds derived from conformal collider physics. I will also discuss applications to holographic theories.