Monica Jinwoo Kang

Strings and Geometry 2024, May 2024

Princeton Center for Theoretical Physics (PCTS) workshop on "Random Physics", March 2024

Isaac Newton Institute (INI) workshop on "Bridges between holographic quantum information and quantum gravity", November 2023

Isaac Newton Institute (INI) program on "Black holes: bridges between number theory and holographic quantum information", November 2023

This is a review talk of my works on operator-algebraic perspective to holography (AdS/CFT).

Title: Infinite-dimensional holography: bulk reconstruction, relative entropy, and operator algebra

Abstract: I will first highlight the advantages of adopting an algebraic approach to understand the AdS/CFT correspondence, emphasizing how the algebra of local operators of quantum field theory (QFT) encodes information about spacetime regions. This approach proves particularly advantageous for addressing realistic quantum field theories with infinite-dimensional Hilbert spaces. I will rephrase bulk reconstruction and relative entropy conservation in this algebraic framework, and then utilize the framework to show that they are equivalent. Notably, I will explain the inherent error-correcting properties that arise naturally within this framework and elaborate on the dictionary I am developing bridging operator algebra and holography. Furthermore, I will explain how the framework can be expanded to include non-perturbative gravitational corrections; in this context approximate bulk reconstruction incorporating gravitational errors can be understood through the lens of the privacy/correctability correspondence, which I will motivate. Finally, I will underscore the effectiveness of this algebraic approach in understanding entanglement wedges in spacetime.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS) workshop on "Complex Lagrangians, Mirror Symmetry, and Quantization", October 2023

Title: Finding isomorphic superconformal field theories

Imperial College London Quiver Meeting Seminar, May 2023

Title: Emergent N=4 supersymmetry from N=1

Abstract: I will construct 4d N=1,2 SCFTs with identical central charges a=c (without a large N limit) via the diagonal gauging of collections of non-Lagrangian Argyres–Douglas and conformal matter theories. Utilizing a particular family of theories from this construction, I will present a four-dimensional N=1 supersymmetric field theory that is dual to the N=4 super Yang--Mills theory with gauge group SU(2n+1) for each n. The dual theory is constructed through the diagonal gauging of the SU(2n+1) flavor symmetry of three copies of a particular Argyres–Douglas theory. This theory flows in the infrared to a strongly-coupled N=1 SCFT that lies on the same conformal manifold as N=4 SYM.

Strings and Geometry 2023, March 2023

Title: 4d SCFTs in different guises: a 6d reveal

Abstract: When do two quantum field theories describe the same physics? I will discuss some approaches to this question in the context of superconformal field theories in four and six dimensions. Utilizing 4d class S theories that also admits 6d (1,0) SCFT origins, I will explain how certain class of 4d N=2 SCFTs, which a priori look like distinct theories, can be shown to describe the same physics, as they arise as torus-compactifications of identical 6d (1,0) SCFTs. Each 6d SCFT in question can be obtained from a parent 6d SCFT by Higgs branch renormalization group flow, and the parent theory possesses a discrete symmetry under which the relevant Higgs branch flows are exchanged. The existence of this discrete symmetry, which may be embedded in an enhanced continuous symmetry, proves that the original pair of class S theories are, in fact, isomorphic.

UC Santa Barbara, KITP, High Energy and Gravity Seminars, November 2022

Title: Counting states with global symmetry

Abstract: I will describe the universal aspect of unitary conformal field theories in the high-temperature limit with a global symmetry group G, where G can be a discrete group or a compact Lie group. I will describe the geometric setup to apply the spurion analysis and explain how we can capture this universal aspect up to a constant factor that depends on the choice of a theory. We consider as examples free field CFTs and holographic CFTs of the RN black holes with and without hair. We find that the RNAdS black hole with non-abelian hair is thermodynamically more stable than the one without hair.

GGI focus week on "Reconstructing the Gravitational Hologram with Quantum Information", July 2022

Title:Bulk reconstruction with nonperturbative gravity

The dual mystery channel of gauge and gravity seminar, IIT-Madras, March 2022

Title: Nonperturbative gravity corrections to bulk reconstruction

Abstract: I will first motivate the benefits on taking the algebraic approach to understand AdS/CFT and how an algebra of local operators of QFT has knowledge of a spacetime region. Utilizing both operator algebras and quantum information theory, I will explain a new framework for understanding nonperturbative gravitational aspects of bulk reconstruction with a finite or infinite-dimensional boundary Hilbert space. This will be understood as approximate recovery containing gravitational errors, and the bulk reconstruction in this context will be understood using the privacy/correctability correspondence.

Rutgers High Energy Theory Group Seminar, December 2021

Title: 4d SCFTs with a=c

Abstract: I will present a particular set of 4d N=2 SCFTs that can be labeled with a pair of Lie groups of type ADE. For specific choices, we get infinitely many theories arising from this construction that have their two central charges to be identical: a=c (without taking any large N limit). Interestingly, the Schur indices of these theories are identical to that of N=4 super Yang-Mills uptown rescaling fugacities. I will further utilize this construction to present various 4d N=1 SCFTs with a=c.

Simons workshop on Geometry of (S)QFT, September 2021

Title: 4d SCFTs with a=c

Abstract: I will present a particular set of 4d N=2 SCFTs that can be labeled with a pair of Lie groups of type ADE. For specific choices, we get infinitely many theories arising from this construction that have their two central charges to be identical: a=c (without taking any large N limit). Interestingly, the Schur indices of these theories are identical to that of N=4 super Yang-Mills uptown rescaling fugacities. I will further utilize this construction to present various 4d N=1 SCFTs with a=c.

The 2nd workshop on Quantum Geometry and Duality, October 2021

Title: Geometric origins and motivations to 4d SCFTs

Based on "Two 6d origins of 4d SCFTs: class S and 6d (1, 0) on a torus (arXiv:2106.11990)" and "Infinitely many 4d N=2 SCFTs with a=c and beyond (arXiv:2106.12579)"

2nd PIMS Summer School on Algebraic Geometry in High Energy Physics, August 2021

Title: Elliptic Fibrations and Singularities to Anomalies and Spectra (4 Lectures)

Abstract: Throughout my lectures I will explain the geometry of elliptic fibration which can gave rise to understanding the spectra and anomalies in lower-dimensional theories from the Calabi-Yau compactifications of F-theory. I will first explain what elliptic fibration is and explain Kodaira types, which gives rise an ADE classification. Utilizing Weierstrass model of elliptic fibrations, I will discuss Tate's algorithm and Mordell-Weil group. By considering codimension one and two singularities and studying the geometry of crepant resolutions, we can define G-models that are geometrically-engineered models from F-theory. I will discuss the dictionary between the gauge theory and the elliptic fibrations and how to incorporate this to learn about topological invariants of the compactified Calabi-Yau that is one of the ingredient to understand spectra in the compactified theories. I will explain the more refined connection to understand the Coulomb branch of the 5d N=1 theories and 6d (1,0) theories and their anomalies from this perspective.

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UC Santa Barbara, KITP, High Energy and Gravity Seminars, March 2021

Title: The infinite HaPPY code and the bulk reconstruction

Abstract: I will construct an infinite-dimensional analog of the HaPPY code as a growing series of stabilizer codes defined respective to their Hilbert spaces. These Hilbert spaces are related by isometries that will be defined during this talk. I will analyze its system in various aspects and demonstrate, using an operator-algebraic perspective, that the bulk reconstruction is satisfied for the infinite-dimensional analogue of the HaPPY code. I will discuss its implications in AdS/CFT and further utilize this operator-algebraic approach to the approximate theorem between the bulk reconstruction and relative entropy equivalence.

UC Berkeley, String Seminar, October 2020

Title: A GNS story of holographic baby universes

Abstract: I will introduce a GNS construction as a formalism to study baby universes. This naturally shifts the primordial role to the algebra of observables rather than the Hilbert spaces. I will explicitly form baby universe operations and utilize them to build baby universe algebras. Using these ingredients, I will construct the baby universe Hilbert spaces. I will highlight that this approach will give an understanding of the miraculous cancellation as a natural result from the character theory. I will illustrate its physics by giving two different physical settings as examples.

UC Santa Barbara, KITP, High Energy and Gravity Seminars, August 2020

Title: Algebras of observables for holographic theories: a GNS story

Perimeter Institute, Fields and Strings Seminar, December 2019

Title: Entanglement wedge reconstruction and operator algebras

Abstract: In order to satisfy the Reeh-Schlieder theorem, I study the infinite-dimensional Hilbert spaces using von Neumann algebras. I will first present the theorem that the entanglement wedge reconstruction and the equivalence of relative entropies between the boundary and the bulk (JLMS) are exactly identical. Then I will demonstrate the entanglement wedge reconstruction with a tensor network model of von Neumann algebra with type II1 factor, which guarantees the equivalence between the boundary and the bulk. I will further sketch that this toy model can be generalized to provide more general von Neumann algebras, including the case of a type III1 factor. This can give further insights to understanding quantum gravity from an algebraic perspective.

IAS Workshop on Qubits and Spacetime, December 2019

Title: Entanglement Wedge Reconstruction in Infinite-Dimensional Hilbert Spaces

Perimeter Institute, Mathematical Physics Seminar, February 2019

Title: Coulomb Phases and Anomalies: Geometric Approach to 5d/6d Theories

Abstract: I will review the geometric approach to the description of Coulomb branches and Chern-Simons terms of gauge theories coming from compactifications of M-theory on elliptically fibered Calabi-Yau threefolds. Mathematically, this involves finding all the crepant resolutions of a given Weierstrass model and understanding the network of flops connecting them together with computing certain topological invariants. I will further check that the uplifted theory in 6d is anomaly-free using Green-Schwartz mechanism. I will give examples on the theory with semi-simple gauge groups such as SU(2)xG2, which plays a major role in the classification of 6d superconformal theories, and SU(2)xSU(3), which describes the non-abelian sector of the standard model.

Simons Center for Geometry and Physics, Physics Seminar, October 2018

Title: Anomaly Cancellation from Geometric Understanding of 5d/6d Spectra

Abstract: I will describe the Coulomb branch of the 5d theory obtained by M-theory compactifications on Calabi-Yau threefolds. I encode non-abelian gauge theories geometrically by using elliptic fibrations on M-theory (that has an F-theory dual). I will describe the spectra of the resulting 5d theories and their 6d uplifts. I will further discuss the anomalies of the uplifted theory.

Strings 2017, June 2017

Title: Euler Characteristics of Crepant Resolutions of Weierstrass Models