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String Seminar

Ground State Entanglement in Long-Range Systems

I will talk about our work investigating the scaling of entanglement entropy in ground states of long-range systems. We study free fermionic lattice models in one-spatial dimension where the hopping and pairing terms decay as a power law with exponent α. In disordered models, we find fractal scaling of entanglement approaching a volume-law as α goes to zero. In models with a continuum limit, the scaling is constrained by predictions from the low-energy theory. There is no universality in the critical α beyond which area-law scaling of local systems is restored. These features are expected to persist in more general system

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Bootstrap bounds on D0-brane quantum mechanics

I derive simple bootstrap bounds on correlation functions of the BFSS matrix theory/D0-brane quantum mechanics. The result strengthens and extends Polchinski’s virial theorem bound to finite energies and gives the first non-trivial bound on 〈TrX2〉. Despite their simplicity, the bounds hint at some features of the dual black hole geometry. The best lower bounds are already a factor of ~ 0.7 from the large N extrapolation of Monte Carlo predictions.

 

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Emergent Area Laws from Entangled Matrices

Arguments such as those due to Susskind and Uglum show that open strings ending on an entangling surface are crucial to understanding the nature of black hole microstates in string theory and the degrees of freedom being partitioned by Ryu-Takayanagi surfaces in holography. We seek an understanding of these edge modes from the perspective of the boundary theory. 

In this talk, we will focus on a particular Matrix Quantum Mechanics model known as mini-BMN that describes an emergent noncommutative Yang-Mills theory on a fuzzy sphere. In mini-BMN and similar models, an analogous problem involves correctly treating the off-diagonal matrix elements that connect eigenvalues on either side of the entanglement cut. We show that these operators, which may be thought of as open strings stretching between D0-branes on either side of the cut, carry representations under the theory's SU(N) symmetry which store information about the size of the entangling surface in the emergent geometry.

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Zoom
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CFT Dual of $dS_3$ and Pseudo Entropy

We propose a holographic duality for gravity on a three-

dimensional de Sitter space. This is essentially given by a $k=-2$ limit

of SU(2) WZW model. We show that this proposal reproduces the expected

free energy in de Sitter gravity. We also analyze the geodesic length in

the three dimensional de Sitter spacetime and argue that it is

interpreted as holographic pseudo entropy. We will also discuss a time-

like entanglement entropy in AdS/CFT which shares a similar property in

terms of pseudo entropy.

Zoom link will be posted shortly before the seminar.

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Zoom
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Mixing local and extended operators: a 2d vertex algebra in 4d N = 2 SCFTs

Algebras of supersymmetry protected local and extended operators can provide analytic access to the dynamics of supersymmetric quantum field theories, even when they are strongly interacting. For example, unitary 4≥ 2 superconformal field theories (SCFTs) contain a protected subsector of local operators, the so-called Schur operators, which produce an associated 2vertex operator algebra (VOA). I will show that one can use these Schur operators to construct a fascinating web of extended operators (lines, surfaces, ...) which exist in every such SCFT. Moreover, these extended operators will mix with the local Schur operators to form a larger algebraic structure called a 2vertex algebra. I will illustrate the richness of this mixed structure explicitly in the case of a free hypermultiplet.

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CP 303
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Emergent averaging in large-N holography

In recent years, a new holographic paradigm has emerged in which simple theories of gravity in low dimensions are dual to statistical ensembles of quantum mechanical systems rather than particular quantum systems. This is a conceptual departure from the conventional holographic paradigm, particularly as realized in string theory. A hallmark of such averaged holographic dualities is the non-factorization of multi-boundary observables due to the presence of Euclidean wormholes in the bulk gravitational theory. However, more realistic holographic dualities in higher dimensions are not expected to fundamentally involve microscopic averaging. Nevertheless, there are apparently contributions to the semiclassical gravitational path integral that are associated with averaging in the boundary theory. In this talk I will attempt to reconcile these perspectives by elucidating the emergence of averaging in two different models based on recent works of mine: one top-down, the other bottom-up. In both cases, averaging of boundary degrees of freedom is an emergent phenomenon associated with the expansion around the semiclassical limit.

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CP 303
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Classification of Unitary RCFTs with Two Primaries and c < 25

I will present a classification of all unitary, rational conformal field theories with two primaries, central charge c < 25, and arbitrary Wronskian index. These are shown to be either certain level-1 WZW models or cosets of meromorphic theories by such models. By leveraging the existing classification of  meromorphic CFTs of central charge c ≤ 24, all the relevant cosets are enumerated and their characters computed. This leads to 123 theories, most of which are new. It will be emphasised that this is a classification of RCFTs and not just consistent characters. Work in collaboration with Brandon Rayhaun.

This is a joint Theory/String seminar.

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CP 303
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