Abstract: In constructing lattice versions of physical theories, usually the spacetime symmetries are given up. This is because of the use of difference approximation of the derivative operator which does not satisfy Leibniz rule. The same is responsible for the fermion doubling problem and the associated loss of chirality. We introduce a non-local lattice derivative, hereafter to be called logarithmic discrete derivative (LDD), as it admits a logarithmic expansion in powers of the difference operator and a formal lattice integral (LI) which is inverse of LDD. The pair (LDD, LI) can be shown to satisfy the same differential and integral calculi of the continuum. We demonstrate how the pair can be used to construct lattice theories with Poincaré invariance. A striking property of the resulting model is a local correspondence which says that local equations of the continuum theory still hold true on the lattice, site-wise. Although such a construction looks very formal in position space, in momentum space the action takes a simple form which may allow for numerical simulations. We show that the same momentum space results can also be obtained by using summation, instead of LI, by using a technique involving finer lattices. Similar concept was earlier arrived at by G. Bergner while studying SLAC-type non-local derivatives. We explain how LDD is related to SLAC derivative and indicate how the new understanding of locality in position space could potentially allow for more effective use of non-local derivatives in lattice studies. Time permitting, we shall also discus a generalisation of the construction to a class of curved backgrounds and another form of the lattice derivative that achieves the same thing but takes the form of an inverse sine hyperbolic function. 

Zoom: https://uky.zoom.us/my/shapere

The finiteness of entanglement entropy in string theory has crucial implications for the information paradox, quantum gravity, and holography. In my talk, I will describe the recent progress made on establishing this finiteness. I will describe the orbifold construction appropriate for analyzing entanglement in string theory, the tachyonic divergences that one encounters and how we get a finite and calculable answer for the entanglement entropy, including ten-dimensional string theory and compactification to lower dimensions. (Based on work in collaboration with Atish Dabholkar.)

I will introduce a critical string theory in two dimensions and demonstrate that this theory, viewed as two-dimensional quantum gravity on the worldsheet, is equivalent to a double-scaled matrix integral, which provides the holographic description. The worldsheet theory consists of Liouville CFT with central charge c >= 25 coupled to timelike Liouville CFT with central charge 26-c. The double-scaled matrix integral has as its leading density of states the universal Cardy density of primaries in a two-dimensional CFT, which gives the theory its name. The talk is based on joint work with Scott Collier, Beatrix Mühlmann and Victor Rodriguez.

This is a Zoom seminar:  https://uky.zoom.us/my/shapere

We will meet in CP 303 to watch it. 

Abstract:  I will describe extremal surfaces in de Sitter space anchored at the future boundary I+. Since such surfaces do not return, they require extra data or boundary conditions in the past (interior). In entirely Lorentzian de Sitter spacetime, this leads to future-past timelike surfaces stretching between I±. Apart from an overall −i factor (relative to spacelike surfaces in AdS) their areas are real and positive. With a no-boundary type boundary condition, the top half of these timelike surfaces joins with a spacelike part on the hemisphere giving a complex-valued area. Motivated by these, we describe two aspects of “time-entanglement” in simple toy models in quantum mechanics. One is based on a future-past thermofield double type state entangling timelike separated states, which leads to entirely positive structures. Another is based on the time evolution operator and reduced transition amplitudes, which leads to complex-valued entropy. There are close parallels with pseudo-entropy which we will clarify.

We will discuss the non-equilibrium dynamics of a 2-dim black hole coupled to an external bath, using the Schwinger-Keldysh formalism. Tracing the evaporation in real time amounts to solving non-local stochastic differential equations for the BH degrees of freedom. We describe the fluctuations that characterise the end point of the evaporation process. This talk is based on arXiv:2210.15579.

We consider the infrared (IR) aspects of S-matrix in QED. We will review IR divergences and their relation to the asymptotic symmetry in QED, and introduce the dressed state formalism to obtain IR-safe S-matrix elements. We show a generic condition (dress code) for dressed states to obtain IR-safe S-matrix elements, and explain that the dress code can be interpreted as the memory effect and represents the superselection rule of asymptotic symmetry.

We discuss  the large N expansion in  the background of extended states focusing on the 

implementation of Goldstone symmetries and the construction of the associated Hilbert space.The large N Thermofield 

provides the main focus, with the emergent dynamics of generalized (free) fields and collective symmetry coordinates

Do the postulates of quantum mechanics survive in quantum gravity?  The probabilistic interpretation of amplitudes, enforced by the unitarity of time evolution, is not guaranteed within the path integral formulation and has to be checked.  Leveraging the gravitational path integral, we find a non-perturbative mechanism whereby a sum over smooth geometries leads to isometric rather than unitary evolution, which we demonstrate in simple models of de Sitter quantum gravity.  These models include Jackiw-Teitelboim gravity and a minisuperspace approximation to Einstein gravity with a positive cosmological constant.  In these models we find that knowledge of bulk physics, even on arbitrarily large timescales, is insufficient to deduce the de Sitter S-matrix.