Erik Verlinde - Academia.edu (original) (raw)

Papers by Erik Verlinde

Research paper thumbnail of Chiral Bosonization, Determinants and the String Partition Function

We study the bosonization of chiral fermion theories on arbitrary compact Riemann surfaces. We ex... more We study the bosonization of chiral fermion theories on arbitrary compact Riemann surfaces. We express the fermionic and bosonic correlation functions in terms of theta functions and prove their equality. This is used to obtain explicit expressions for a class of chiral determinants ...

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Research paper thumbnail of A Conversation on ER = EPR

arXiv (Cornell University), Dec 19, 2022

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Research paper thumbnail of Passing through the Firewall

arXiv (Cornell University), Jun 3, 2013

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Research paper thumbnail of Notes on matrix and micro strings

Nuclear physics, Nov 1, 1998

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Research paper thumbnail of Conformal Field Theory and Geometric Quantization

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Research paper thumbnail of Loop Equations and Virasoro Constraints in Non-Perturbative Two-Dimensional Quantum Gravity

WORLD SCIENTIFIC eBooks, Aug 1, 1993

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Research paper thumbnail of Strings '97, Proceedings of the International Conference held at the University of Amsterdam, Amsterdam, June 16-21, 1997

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Research paper thumbnail of Passing through the Firewall

arXiv (Cornell University), Jun 3, 2013

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Research paper thumbnail of Notes on Matrix Strings and Fivebranes

Dualities in Gauge and String Theories, 1998

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Research paper thumbnail of Black hole entanglement and quantum error correction

Journal of High Energy Physics, 2013

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Research paper thumbnail of Quantum chaos in 2D gravity

arXiv (Cornell University), Apr 15, 2022

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Research paper thumbnail of Conformal field theory and its application to strings

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Research paper thumbnail of Hartle-Hawking Wave-Function for Flux Compactifications

We argue that the topological string partition function, which has been known to correspond to a ... more We argue that the topological string partition function, which has been known to correspond to a wave-function, can be interpreted as an exact ``wave-function of the universe'' in the mini-superspace sector of physical superstring theory. This realizes the idea of Hartle and Hawking in the context of string theory, including all loop quantum corrections. The mini-superspace approximation is justified as an exact description of BPS quantities. Moreover this proposal leads to a conceptual explanation of the recent observation that the black hole entropy is the square of the topological string wave-function. This wave-function can be interpreted in the context of flux compactification of all spatial dimensions as providing a physical probability distribution on the moduli space of string compactification. Euclidean time is realized holographically in this setup.

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Research paper thumbnail of and Quantum Error Correction

It was recently argued in [1] that black hole complementarity strains the basic rules of quantum ... more It was recently argued in [1] that black hole complementarity strains the basic rules of quantum information theory, such as monogamy of entanglement. Motivated by this argument, we develop a practical framework for describing black hole evaporation via uni-tary time evolution, based on a holographic perspective in which all black hole degrees of freedom live on the stretched horizon. We model the horizon as a unitary quantum system with finite entropy, and do not postulate that the horizon geometry is smooth. We then show that, with mild assumptions, one can reconstruct local effective field theory observables that probe the black hole interior, and relative to which the state near the horizon looks like a local Minkowski vacuum. The reconstruction makes use of the formalism of quantum error correcting codes, and works for black hole states whose entanglement entropy does not yet saturate the Bekenstein-Hawking bound. Our general framework clarifies the black hole final state propo...

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Research paper thumbnail of No Page Curves for the de Sitter Horizon

We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from thre... more We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from three-dimensional pure de Sitter space, we consider a partial reduction approach, which supplies an auxiliary system acting as a heat bath both at future infinity and inside the static patch. This allows us to study the time-dependent entropy of radiation collected for both observers in the out-of-equilibrium Unruh-de Sitter state, analogous to black hole evaporation for a cosmological horizon. Central to our analysis in the static patch is the identification of a weakly gravitating region close to the cosmological horizon; this is suggestive of a relation between observables at future infinity and inside the static patch. We find that in principle, while the meta-observer at future infinity naturally observes a pure state, the static patch observer requires the use of the island formula to reproduce a unitary Page curve. However, in practice, catastrophic backreaction occurs at the Page tim...

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Research paper thumbnail of Loop Equations and Virasoro Constraints in Non-perturbative 2-D Quantum Gravity

We give a derivation of the loop equation for two-dimensional gravity from the KdV equations and ... more We give a derivation of the loop equation for two-dimensional gravity from the KdV equations and the string equation of the one matrix model. We find that the loop equation is equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the Virasoro algebra. We give an interpretation of these equations in topological gravity and discuss their extension to multi-matrix models. For the multi-critical models the loop equation naturally singles out the operators corresponding to the primary fields of the minimal models.

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Research paper thumbnail of Comments on ”On the Origin of Gravity and the

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Research paper thumbnail of Notes on Topological String Theory and 2D Quantum Gravity

In these notes we give a review of topological string theory. We discuss two-dimensional topologi... more In these notes we give a review of topological string theory. We discuss two-dimensional topological eld theories, which represent its classical backgrounds. We describe their symmetries and the properties of the physical amplitudes. In the particular context of d < 1 we explain how topological string theory can be exactly solved, by deriving Schwinger-Dyson equations in the form of recursion relations between world-sheet correlation functions at different genera.

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Research paper thumbnail of From the BTZ black hole to JT gravity: geometrizing the island

Journal of High Energy Physics

We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional po... more We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. A partial dimensional reduction of AdS3 in Poincaré coordinates leads to an extremal 2D black hole in JT gravity coupled to a ‘bath’: the holographic dual of the remainder of the 3D spacetime. Partially reducing the BTZ black hole gives us the finite temperature version. We compute the entropy of the radiation using geodesics in the three-dimensional spacetime. We then focus on the finite temperature case and describe the dynamics by introducing time-dependence into the parameter controlling the reduction. The energy of the black hole decreases linearly as we slowly move the dividing line between black hole and bath. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. Finally, studying the entropy of the radiation over time leads to a geometric representation of the Page curve. The appearance of the island region i...

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Research paper thumbnail of arXiv : Probing typical black hole microstates

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Research paper thumbnail of Chiral Bosonization, Determinants and the String Partition Function

We study the bosonization of chiral fermion theories on arbitrary compact Riemann surfaces. We ex... more We study the bosonization of chiral fermion theories on arbitrary compact Riemann surfaces. We express the fermionic and bosonic correlation functions in terms of theta functions and prove their equality. This is used to obtain explicit expressions for a class of chiral determinants ...

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Research paper thumbnail of A Conversation on ER = EPR

arXiv (Cornell University), Dec 19, 2022

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Research paper thumbnail of Passing through the Firewall

arXiv (Cornell University), Jun 3, 2013

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Research paper thumbnail of Notes on matrix and micro strings

Nuclear physics, Nov 1, 1998

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Research paper thumbnail of Conformal Field Theory and Geometric Quantization

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Research paper thumbnail of Loop Equations and Virasoro Constraints in Non-Perturbative Two-Dimensional Quantum Gravity

WORLD SCIENTIFIC eBooks, Aug 1, 1993

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Research paper thumbnail of Strings '97, Proceedings of the International Conference held at the University of Amsterdam, Amsterdam, June 16-21, 1997

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Research paper thumbnail of Passing through the Firewall

arXiv (Cornell University), Jun 3, 2013

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Research paper thumbnail of Notes on Matrix Strings and Fivebranes

Dualities in Gauge and String Theories, 1998

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Research paper thumbnail of Black hole entanglement and quantum error correction

Journal of High Energy Physics, 2013

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Research paper thumbnail of Quantum chaos in 2D gravity

arXiv (Cornell University), Apr 15, 2022

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Research paper thumbnail of Conformal field theory and its application to strings

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Research paper thumbnail of Hartle-Hawking Wave-Function for Flux Compactifications

We argue that the topological string partition function, which has been known to correspond to a ... more We argue that the topological string partition function, which has been known to correspond to a wave-function, can be interpreted as an exact ``wave-function of the universe'' in the mini-superspace sector of physical superstring theory. This realizes the idea of Hartle and Hawking in the context of string theory, including all loop quantum corrections. The mini-superspace approximation is justified as an exact description of BPS quantities. Moreover this proposal leads to a conceptual explanation of the recent observation that the black hole entropy is the square of the topological string wave-function. This wave-function can be interpreted in the context of flux compactification of all spatial dimensions as providing a physical probability distribution on the moduli space of string compactification. Euclidean time is realized holographically in this setup.

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Research paper thumbnail of and Quantum Error Correction

It was recently argued in [1] that black hole complementarity strains the basic rules of quantum ... more It was recently argued in [1] that black hole complementarity strains the basic rules of quantum information theory, such as monogamy of entanglement. Motivated by this argument, we develop a practical framework for describing black hole evaporation via uni-tary time evolution, based on a holographic perspective in which all black hole degrees of freedom live on the stretched horizon. We model the horizon as a unitary quantum system with finite entropy, and do not postulate that the horizon geometry is smooth. We then show that, with mild assumptions, one can reconstruct local effective field theory observables that probe the black hole interior, and relative to which the state near the horizon looks like a local Minkowski vacuum. The reconstruction makes use of the formalism of quantum error correcting codes, and works for black hole states whose entanglement entropy does not yet saturate the Bekenstein-Hawking bound. Our general framework clarifies the black hole final state propo...

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Research paper thumbnail of No Page Curves for the de Sitter Horizon

We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from thre... more We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from three-dimensional pure de Sitter space, we consider a partial reduction approach, which supplies an auxiliary system acting as a heat bath both at future infinity and inside the static patch. This allows us to study the time-dependent entropy of radiation collected for both observers in the out-of-equilibrium Unruh-de Sitter state, analogous to black hole evaporation for a cosmological horizon. Central to our analysis in the static patch is the identification of a weakly gravitating region close to the cosmological horizon; this is suggestive of a relation between observables at future infinity and inside the static patch. We find that in principle, while the meta-observer at future infinity naturally observes a pure state, the static patch observer requires the use of the island formula to reproduce a unitary Page curve. However, in practice, catastrophic backreaction occurs at the Page tim...

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Research paper thumbnail of Loop Equations and Virasoro Constraints in Non-perturbative 2-D Quantum Gravity

We give a derivation of the loop equation for two-dimensional gravity from the KdV equations and ... more We give a derivation of the loop equation for two-dimensional gravity from the KdV equations and the string equation of the one matrix model. We find that the loop equation is equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the Virasoro algebra. We give an interpretation of these equations in topological gravity and discuss their extension to multi-matrix models. For the multi-critical models the loop equation naturally singles out the operators corresponding to the primary fields of the minimal models.

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Research paper thumbnail of Comments on ”On the Origin of Gravity and the

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Research paper thumbnail of Notes on Topological String Theory and 2D Quantum Gravity

In these notes we give a review of topological string theory. We discuss two-dimensional topologi... more In these notes we give a review of topological string theory. We discuss two-dimensional topological eld theories, which represent its classical backgrounds. We describe their symmetries and the properties of the physical amplitudes. In the particular context of d < 1 we explain how topological string theory can be exactly solved, by deriving Schwinger-Dyson equations in the form of recursion relations between world-sheet correlation functions at different genera.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of From the BTZ black hole to JT gravity: geometrizing the island

Journal of High Energy Physics

We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional po... more We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. A partial dimensional reduction of AdS3 in Poincaré coordinates leads to an extremal 2D black hole in JT gravity coupled to a ‘bath’: the holographic dual of the remainder of the 3D spacetime. Partially reducing the BTZ black hole gives us the finite temperature version. We compute the entropy of the radiation using geodesics in the three-dimensional spacetime. We then focus on the finite temperature case and describe the dynamics by introducing time-dependence into the parameter controlling the reduction. The energy of the black hole decreases linearly as we slowly move the dividing line between black hole and bath. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. Finally, studying the entropy of the radiation over time leads to a geometric representation of the Page curve. The appearance of the island region i...

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Research paper thumbnail of arXiv : Probing typical black hole microstates

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