We consider a massive scalar, neutral, field theory in a five dimensional flat spacetime. Subsequently, one spatial dimension is compactified on a circle, $S^1$, of radius R. The resulting theory is defined in the manifold, $R^{3,1}\otimes S^1$, consists of a states of lowest mass, $m_0$, and a tower of massive Kaluza-Klein states. The analyticity property of the elastic scattering amplitude is investigated in the frame works of Lehmann-Symanzik-Zimmermann formulation of this field theory. In the context of nonrelativistic potential scattering, for $R^3\otimes S^1$ spatial geometry, it was shown that the forward scattering amplitude does not satisfy analyticity for a class of potentials which might have important consequences if same attribute holds in relativistic quantum field theories. We address this issue with $R^{3,1}\otimes S^1$ geometry. We show that the forward scattering amplitude of the theory satisfying LSZ axioms does not suffer from lack of analyticity. The importance of the unitarity constraint is exhibited in displaying the properties of the absorptive part of the forward amplitude.

We argue that the SYK model leads to a three dimensional dual theory in a suitable background. At strong coupling, a Horava-Witten compactification of one of the dimensions reproduces the SYK spectrum, and a non-standard propagator of the 3D theory exactly reproduces the two point function of the bilocal fields. Furthermore, this three dimensional picture reproduces the leading finite coupling correction to the “zero mode” contribution. The space-time on which the bilocal fields live is not, however, the dual space-time in the sense of AdS/CFT duality – rather the bilocals are related to the dual fields by an integral transform.

The understanding of out-of-equilibrium physics, especially dynamic instabilities and phase transitions, is one of the major challenges of contemporary science. Focusing on non-equilibrium dynamics of open dissipative spin systems, I will introduce non-Hermitian Hamiltonian formalism, in which anti-Hermiticity reflects dissipation and presence of non-conservative forces. I will discuss a special case of parity-time-symmetric Hamiltonians that exhibit a phase transition from real to complex eigenspectrum, and how it manifests experimentally. I will then illustrate branch point singularities that appear in the spectrum of some non-Hermitian Hamiltonians, and show how these so-called exceptional points provide access to a wealth of topological effects unique to non-Hermitian systems, e.g. asymmetric transport and non-reciprocal time evolution.

I'll talk about the operator algebra view of entanglement and its connection to more down-to-earth calculational ways of understanding it. This talk will be a pedagogical introduction to the subject.

The interplay of symmetry and topology has been at the forefront of recent progress in quantum matter. In this talk I will discuss an unexpected connection between band topology and competing orders in a quantum magnet. The key player is the two-dimensional Dirac spin liquid (DSL), which at low energies is described by an emergent Quantum Electrodynamics with massless Dirac fermions (a.k.a. spinons) coupled to a U(1) gauge field. A long-standing open question concerns the symmetry properties of the magnetic monopoles, an important class of critical degrees of freedom. I will show that the monopole properties can be determined from the topology of the underlying spinon band structure. In particular, the lattice momentum and angular momentum of monopoles can be determined from the charge (or Wannier) centers of the corresponding spinon insulators. I will then discuss the consequences of the monopole properties, such as the stability of the DSL on different lattices, universal (experimental and numerical) signatures of DSL, and competing symmetry-breaking phases near the DSL state.

The Rényi entanglement entropy of quantum many-body systems can be viewed as the difference in free energy of partition functions with different trace topologies. We introduce an external field λ that controls the partition function topology, allowing us to define a notion of nonequilibrium work as λ is varied smoothly. Nonequilibrium fluctuation theorems of the work provide us with statistically exact estimates of the Rényi entanglement entropy. We put these ideas to use in the context of quantum Monte Carlo simulations of SU(N) symmetric spin models in one and two dimensions. In both cases we detect logarithmic violations to the area law with high precision, allowing us to extract the central charge for the critical 1D models and the number of Goldstone modes for the magnetically ordered 2D models.

I will discuss global quenches in a number of interacting quantum field theory models away from the conformal regime. The scaling of various observables at early times will be presented with a particular emphasis placed on the leading order effects that cannot be recovered using the finite order conformal perturbation theory. At the end I will discuss potential route towards understanding the late time dynamics using the canonical ideas of effective action.

In this talk I shall be describing how to obtain planar scattering amplitudes of quartic massless scalar theory from some particular positive geometries known as Stokes polytopes. The residues of the canonical form on these Stokes polytopes can be used to compute scattering amplitudes for quartic interactions. Properties like locality and unitarity of the amplitudes will be manifest from the geometric properties of the Stokes polytopes.

The SYK model provides an uncommon example of a theory where Eigenstate Thermalization Hypothesis (ETH) can be verified in analytically. In this talk I will discuss this model in the deep infrared limit where the theory has an emergent conformal (reparametrization) symmetry that is broken both spontaneously and explicitly. To study the validity of ETH, we compute the heavy- light correlation functions of operators in the conformal spectrum of the theory. We compute these correlation functions with and without the contribution of the low energy (Schwarzian) modes, which are known to be the origin of the chaotic behaviour in this theory. In considering the contributions of the Schwarzian modes we find a weaker form of ETH: while the heavy operator insertions increase the effective temperature perceived by the light insertions, this effective temperature is proportional to the background temperature and goes to zero with the background temperature. In the case where Schwarzian modes aren’t considered, we find ETH in limit in which the weight of the heavy operators approach infinity. I will also discuss implications of these results for the states in AdS2 gravity dual.