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We study chiral algebras associated with Argyres-Douglas theories engineered from M5 brane. For the theory engineered using 6d (2,0) type J theory on a sphere with a single irregular singularity (without mass parameter), its chiral algebra is the minimal model of W algebra of JJ type. For the theory engineered using an irregular singularity and a regular full singularity, its chiral algebra is the affine Kac-Moody algebra of JJ type. We can obtain the Schur and Hall-Littlewood index of these theories by computing the vacua character of the corresponding chiral algebra.

Lack of fine tuning in effective field theory does not ensure that a particular scenario is natural or even realizable in a UV complete theory of quantum gravity. Large field axion inflation appears natural from the effective field theory perspective, but I argue that it is tuned from a quantum gravity perspective. The argument is based on the Weak Gravity Conjecture (WGC), a conjectural universal feature of quantum gravity that is present in all known string theory examples. In the process, I highlight recent progress in understanding the WGC and related conjectures about the charged spectrum of quantum gravity and discuss other potential applications, both formal and phenomenological.

It has long been wondered to what extent the observable properties of an inhomogeneous universe will be measurably different from a corresponding FLRW model. Here, we use tools from numerical relativity to study the properties of photons traversing an inhomogeneous universe. We evolve the full, unconstrained Einstein field equations for a spacetime containing dust, with a spectrum of long-wavelength density perturbations similar to the observed one. We then integrate the optical scalar equations along paths through this numerical spacetime, with all paths terminating at an observer situated similarly to ourselves, and construct the resulting Hubble diagrams.

I will talk about some connections among the GKZ (introduced by Gelfand-Kapranov-Zelevinsky) hypergeometric series, orbifold singularities of the system, and chain integrals in some geometry.  The GKZ hypergeometric series appeared in some very interesting contexts including arithmetic geometry, enumerative geometry and mathematical physics in the last few decades. I will report some new geometric realizations and interpretations of them.

In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study local quantum many-body systems at low energies. 

In this talk, I will describe how a tensor network representation of a quantum many-body ground state also encodes, in a natural way, another quantum many-body state whose properties must be related to the ground state in a systematic way. One can apply this tensor network state correspondence to the multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a one dimensional (1D) quantum lattice system to obtain a quantum many-body state of a 2D hyperbolic quantum lattice, whose boundary is the original 1D lattice. I propose that this bulk/boundary correspondence could potentially be a candidate implementation of the holographic correspondence of String theory on a lattice using the MERA.

For the MERA representation of a critical ground state I will show how the critical properties can be obtained from the corresponding bulk state, in particular, illustrating how point-like boundary operators are identified with extended operators in the bulk. I will also describe the entanglement and correlations in the bulk state, present numerical results that illustrate that the bulk entanglement may depend on the boundary critical charge, and describe how the bulk state can be described in terms of "holographic screens". If the boundary state has a global symmetry, the corresponding bulk state has a local gauge symmetry (described by the same group). In fact, the bulk state decomposes in terms of spin networks as they appear in lattice gauge theory, where they describe the gauge-invariant sector of the theory (here, the bulk). This decomposition also reveals entanglement between gauge degrees of freedom in the bulk, which are dual to a global symmetry at the  boundary, and remaining bulk degrees of freedom which may potentially include gravitational degrees of freedom in a holographic interpretation of the MERA.