Holographic duality

The gauge/gravity duality was proposed in late 1990s as an equivalence between a gravitational theory and a quantum field theory, where the quantum theory has no gravity and lives in a spacetime with one less dimension than the gravity theory. In analogy to holograms in which 3D images are encoded in 2D, the duality also became known as holographic duality. The holographic duality has passed many tests and improvements on a dictionary that translates the physical objects in the two theories, and it has become a valuable tool in the investigation of problems from quantum gravity to those in strongly interacting quantum many-body physics. The Ryu-Takayanagi prescription is one special entry in this dictionary that relates entanglement entropy in a quantum theory to surfaces of minimal areas as the dual gravitational object. This remarkable result opened up a strong interdisciplinary link connecting gravity to the condensed matter and quantum information theory communities.

Traversable wormholes

Another remarkable result within the context of the holographic duality was an explicit construction of a traversable wormhole, where such wormhole can be viewed as two black holes whose interiors are connected by a “throat”. It is well known that traversable wormholes are classically forbidden according to Einstein’s theory of general relativity because they violate energy conditions we expect matter to obey, but in this new construction a coupling between the two asymptotic boundaries of the wormhole is introduced in such a way that the assumptions of the energy theorems no longer apply. Traversable wormholes are still under active investigation, specially its dual in the quantum theory side of the duality. So far, the most accepted interpretation states that the process of sending some matter/information through the wormhole is dual to a quantum teleportation protocol.

Sachdev-Ye-Kitaev (SYK) model

The Sachdev-Ye-Kitaev (SYK) model is a quantum many-body system that displays an emergent gravitational behavior when the number of particles, $N$, is very large. This model has been successful as a concrete solvable model in the investigation of quantum gravity by providing several insights on problems such as the black hole interior, the construction of traversable wormholes, and the quantum chaotic nature of black holes. A natural question is how this model transitions from a quantum mechanical to a gravitational system as we increase the system size. However, the all-to-all nature of their interactions and the exponentially increasing dimension of the Hilbert space with respect to the system size makes the investigation of SYK intractable in this regime, where there is no analytical control and numerical simulations are restricted to small sizes even when advanced numerical techniques are employed. A variant of this model, dubbed sparse SYK, recently appeared in the literature. It drastically reduces the number of interaction terms to be only of order $N$, while still preserving the essential properties that make the SYK model a good gravity dual. The sparse SYK model then arises as a much more computationally tractable model of holographic duality and provides an excellent avenue for exploring the emergence of gravity from a quantum mechanical system.

• Mexicuerdas 2017 “Traversable wormholes” (Slides)

• APS 2018 Houston “Rotating traversable wormholes in AdS” (Slides)

• Southwest Strings 2019 “Entanglement & Causal Wedge in Gauss-Bonnet gravity” (Slides)

• Southwest Strings 2020 “Causal structure of Multiboundary Wormholes” (Slides)

• Southwest String Meeting 2021 “Traversable Wormholes from a sparse SYK model” (Slides)

• II Siembra-HoLAGrav Young Frontiers 2021 “Sparse SYK and traversable wormholes” (Slides)

Assistant Instructor - University of Texas at Austin

• PS 304 Introductory Physical Science II (Fall 2020 - Spring 2020)

Teaching Assistant - University of Texas at Austin

• PHY 317L General Physics I (Spring 2022)
• PHY 317L General Physics II (Fall 2021)
• PHY 352K Classical Electrodynamics I (Spring 2019)
• PHY 373 Quantum Physics I (Fall 2018)
• PHY 117M Laboratory for Physics 317K (Fall 2016 - Spring 2018)