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This course provides a thorough introduction to the bosonic string based on the Polyakov path integral and conformal field theory. We introduce central ideas of string theory, the tools of conformal field theory, the Polyakov path integral, and the covariant quantization of the string. We discuss string interactions and cover the tree-level and one loop amplitudes. More advanced topics such as T-duality and D-branes will be taught as part of the course. The course is geared for M.Sc. and Ph.D. students enrolled in Collaborative Ph.D. Program in Theoretical Physics. Required previous course work: Quantum Field Theory (AM516 or equivalent). The course evaluation will be based on regular problem sets that will be handed in during the term. The primary text is the book: 'String theory. Vol. 1: An introduction to the bosonic string. J. Polchinski (Santa Barbara, KITP) . 1998. 402pp. Cambridge, UK: Univ. Pr. (1998) 402 p.' All interested students should contact Alex Buchel at abuchel@uwo.ca as soon as possible.

This course provides a thorough introduction to the bosonic string based on the Polyakov path integral and conformal field theory. We introduce central ideas of string theory, the tools of conformal field theory, the Polyakov path integral, and the covariant quantization of the string. We discuss string interactions and cover the tree-level and one loop amplitudes. More advanced topics such as T-duality and D-branes will be taught as part of the course. The course is geared for M.Sc. and Ph.D. students enrolled in Collaborative Ph.D. Program in Theoretical Physics. Required previous course work: Quantum Field Theory (AM516 or equivalent). The course evaluation will be based on regular problem sets that will be handed in during the term. The primary text is the book: 'String theory. Vol. 1: An introduction to the bosonic string. J. Polchinski (Santa Barbara, KITP) . 1998. 402pp. Cambridge, UK: Univ. Pr. (1998) 402 p.' All interested students should contact Alex Buchel at abuchel@uwo.ca as soon as possible.

We derive a universal upper bound on the weight of the lowest primary operator in any two-dimensional conformal field theory with a given central charge. Translated into gravitational language using the AdS/CFT dictionary, our result proves rigorously that the lightest massive state in any theory of 3D gravity and matter with negative cosmological constant can be no heavier than a particular function the cosmological constant and the Planck scale. For a large AdS space, the lower bound approaches the mass of the lightest BTZ black hole. The derivation applies at finite central charge and does not rely on an asymptotic expansion at large central charge, or on any use of semiclassical or bulk physics. Neither does our proof rely on any special property of the CFT such as supersymmetry or holomorphic factorization. The only assumptions are unitarity, modular invariance, and a discrete spectrum. Our proof firmly demonstrates for the first time that there exists a universal center-of-mass energy beyond which a theory of 'pure' quantum gravity can never consistently be extended.

Fundamental interactions between elementary particles, using deep ideas involving mathematical symmetry for restoring unity to the fundamental laws of nature (strong and weak nuclear forces, electromagnetism and gravity).

String theory, the high energy frontier of elementary particle physics, grand unifications into a single framework, mathematical beauty and supersymmetries, and uncovering the quantum structures of space and time.

In this talk, I start with a short review of the available mechanisms for extracting energy from rotating black holes, in particular superradiance and the Blandford-Znajek process. I then describe how these mechanisms may be realized and studied via the AdS/CFT and Kerr/CFT correspondence.

We consider the problem of how fast a quantum system can scramble (thermalize) information, given that the interactions are between bounded clusters of degrees of freedom. Based on previous work, we conjecture: 1) The most rapid scramblers take a time logarithmic in the number of degrees of freedom. 2)Matrix quantum mechanics (systems whose degrees of freedom are n by n matrices) saturate the bound. 3) Black holes are the fastest scramblers in nature. The conjectures are based on the principle of black hole complementarily, quantum information theory, and the study of black holes in string theory. This talk is based on Y. Sekino and L. Susskind, arXiv:0808.2096 [hep-th].

Holography is usually applied to black holes that are supersymmetric, charged, or living in higher dimensions. The astrophysical Kerr black holes that have been observed in the sky have none of these nice properties, and AdS/CFT does not apply. Nevertheless, by studying the symmetries of the near horizon region, I will show that extreme Kerr black holes are holographically dual to a two-dimensional conformal field theory. The U(1) isometry of the near horizon region extends asymptotically to a Virasoro algebra. We compute the central charge semiclassically, and find in particular that the observed black hole GRS 1915+105 is approximately dual to a CFT with central charge 10^79. The microstate counting of the dual CFT correctly reproduces the Bekenstein-Hawking entropy. I will also discuss generalizations to a wide variety of extreme black holes in assorted theories, the possibility of moving away from the external limit, and potential applications of the correspondence.

I'll discuss information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the 'half-way' point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. The resulting estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementary hypothesis. (Joint work with John Preskill).

We present new results from our Monte Carlo simulation of SUSY matrix quantum mechanics with 16 supercharges at finite temperature. The internal energy can be fitted nicely to the behavior predicted from the dual black hole thermodynamics including the alpha' corrections. The temporal Wilson loop can also be predicted from the gravity side, and it is directly related to the Schwarzschild radius of the dual black hole geometry. Our results for the Wilson loop indeed confirm this prediction up to subleading terms anticipated from the alpha' corrections on the gravity side. All these results give us strong support and a firm basis for the idea to use matrix model simulations to study quantum gravity.

I'll discuss some large N quantum mechanical theories that are toy models for eternal black holes in AdS via gauge/gravity duality. They can be used to study the classical limit and quantum corrections in gravity, and their roles in the information paradox. We demonstrate that such large N models can exhibit late time fall-off of a two-point function. By computing higher genus corrections explicitly, we argue that the fall-off, and thus information loss, persist even after perturbative gravity corrections are included.

I will classify the options to solve the black hole information loss problem by how radical a departure from semi-classical gravity they require outside the quantum gravitational regime. I will argue that the most plausible and conservative conclusion is that the problem of information loss originates in the presence of the singularity and that thus effort should be focused on understanding its avoidance. A consequence of accepting the accuracy of the semi-classical approximation is the surface interpretation of black hole entropy. I will summarize the arguments that have been raised for and against such scenarios. Reference: http://arxiv.org/abs/0901.3156