This page is for posting Lecture Notes, Problems Sets, Errata, Open Questions, and a Bibliography.

Note: During this lecture I mistakenly attributed the path integral derivation of Rindler wedge thermality. The correct reference is Unruh and Weiss (not Wald). This mistake has been corrected in the lecture notes. Also, the actual lecture ended around 1.6, the rest will be covered next time.

Note: The recording of the lecture muddled the algebra of the Casini-Huerta proof of the c-theorem a bit, although the main ideas were all correct. It should be patched up in the notes, although you may prefer to get it directly from their paper (see bibliography).

Note: the proof of LM had some wrong signs, but I've fixed it in the scanned lecture notes. (But I made no effort to get the numerical coefficients right.) The notes also include a couple of pages of bonus material on the laws of black hole thermodynamics, not covered in class.

Lecture 6, followed by Discussion thereafter.

Note: My original lecture notes leave off at 5.2, but the last 5 pages of notes refer to a talk I gave on the quantum focussing conjecture. This goes into more detail than I discussed it during the Discussion, but it may provide some helpful context. I had no written notes for the "information puzzle" discussion, so please consult the video of the Discussion for that.

Nabil Iqbal, "Entanglement Entropy in Field Theory and Gravity"

Raphael Bousso, Zachary Fisher, Stefan Leichenauer, and Aron C. Wall, "A Quantum Focussing Conjecture"

Sergey N. Solodukhin, "Entanglement entropy of black holes''

J. Aczél, B. Forte and C. T. Ng, Why the Shannon and Hartley Entropies Are 'Natural'

Imre Csiszár, "Axiomatic Characterizations of Information Measures"

W. Ochs, "A new axiomatic characterization of the von Neumann entropy"

Alain Connes, Noncommutative Geometry, Ch. 5.

Haag, *Local Quantum Physics* (Springer Verlag, Berlin, 1992).

H. J. Borchers, "On revolutionizing quantum field theory with Tomita’s modular theory"

Curtis Callan, Frank Wilczek, "On Geometric Entropy"

C. Holzhey, F. Larsen, and F. Wilczek, "Geometric and renormalized entropy in conformal field theory"

S. N. Solodukhin, "The conical singularity and quantum corrections to entropy of black hole"

P. Calabrese and J. L. Cardy,
"Entanglement entropy and quantum field theory"

"Entanglement entropy and quantum field theory: A Non-technical introduction"

"Entanglement entropy and conformal field theory"

J. Cardy, O. Castro-Alvaredo, and B. Doyon, "Form factors of branch-point twist fields in quantum integrable models and entanglement entropy"

Luca Bombelli, Rabinder K. Koul, Joohan Lee, and Rafael D. Sorkin, "Quantum source of entropy for black holes"

Mark Srednicki, "Entropy and Area"

J. Eisert, M. Cramer, M.B. Plenio, "Area laws for the entanglment entropy - a review"

Pablo Bueno, Robert C. Myers, Corner contributions to holographic entanglement entropy

Dmitri V. Fursaev, Alexander Patrushev, Sergey N. Solodukhin, "Distributional Geometry of Squashed Cones"

Shinsei Ryu, Tadashi Takayanagi, "Aspects of Holographic Entanglement Entropy"

Tatsuma Nishioka, Shinsei Ryu, Tadashi Takayanagi, "Holographic Entanglement Entropy: An Overview"

Matthew Headrick, Tadashi Takayanagi, "A holographic proof of the strong subadditivity of entanglement entropy"

Veronika E. Hubeny, Mukund Rangamani, Tadashi Takayanagi, "A Covariant Holographic Entanglement Entropy Proposal"

Aron C. Wall, "Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy"

Aitor Lewkowycz, Juan Maldacena, "Generalized gravitational entropy"

Thomas Faulkner, Aitor Lewkowycz, Juan Maldacena, "Quantum corrections to holographic entanglement entropy"

Netta Engelhardt, Aron C. Wall, "Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime"

Ted Jacobson, Gungwon Kang, Robert C. Myers "On Black Hole Entropy"

V. Iyer and R. M. Wald, "Some properties of Noether charge and a proposal for dynamical black hole entropy"

V. Iyer and R. M. Wald, "A Comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes"

Xi Dong, "Holographic Entanglement Entropy for General Higher Derivative Gravity"

Rong-Xin Miao, "Universal Terms of Entanglement Entropy for 6d CFTs"

Aron C. Wall, "A Second Law for Higher Curvature Gravity"

William Donnelly,
"Decomposition of entanglement entropy in lattice gauge theory"

"Entanglement entropy and nonabelian gauge symmetry"

Horacio Casini, Marina Huerta, Jose Alejandro Rosabal, "Remarks on entanglement entropy for gauge fields"

William Donnelly, Aron C. Wall
"Entanglement entropy of electromagnetic edge modes"

"Geometric entropy and edge modes of the electromagnetic field"

"A finite entanglement entropy and the c-theorem"

G. Vidal, J. I. Latorre, E. Rico, A. Kitaev, "Entanglement in quantum critical phenomena"

Tarun Grover, "Chiral Symmetry Breaking, Deconfinement and Entanglement Monotonicity"

Cesar A. Agon, Matthew Headrick, Daniel L. Jafferis, Skyler Kasko, "Disk entanglement entropy for a Maxwell field"

Tarun Grover, Yi Zhang, Ashvin Vishwanath, "Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids"

Aitor Lewkowycz,
"Holographic Entanglement Entropy and Confinement"

Aron Wall's Homepage

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You can email me by using my first name, followed by my last name, followed by umd.edu (a***w***@umd.edu).