# Horowitz, Polchinski ## Self-gravitating fundamental strings \[Links: [arXiv](https://arxiv.org/abs/hep-th/9707170), [PDF](https://arxiv.org/pdf/hep-th/9707170.pdf)\] \[Abstract: \] ## Refs - this is OG of [[0323 Horowitz-Polchinski solution]] # Kashaev ## Quantization of Teichmüller spaces and the quantum dilogarithm \[Links: [arXiv](https://arxiv.org/abs/q-alg/9705021), [PDF](https://arxiv.org/pdf/q-alg/9705021)\] \[Abstract: The [[0626 Teichmuller TQFT|Teichmüller space]] of punctured surfaces with the Weil-Petersson symplectic structure and the action of the mapping class group is realized as the Hamiltonian reduction of a finite dimensional symplectic space where the mapping class group acts by symplectic rational transformations. Upon quantization the corresponding (projective) representation of the mapping class group is generated by the quantum dilogarithms.\] # Kitaev ## Fault-tolerant quantum computation by anyons \[Links: [arXiv](https://arxiv.org/abs/quant-ph/9707021), [PDF](https://arxiv.org/pdf/quant-ph/9707021.pdf)\] \[Abstract: A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.\] ## Ref - [[0637 Kitaev code]] # Maldacena ## The large N limit of superconformal field theories and supergravity \[Links: [arXiv](https://arxiv.org/abs/hep-th/9711200), [PDF](https://arxiv.org/pdf/hep-th/9711200.pdf)\] \[Abstract: We show that the large $N$ limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing [[0332 Supergravity|supergravity]] on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large $N$. The enhanced [[0359 Supersymmetry|supersymmetries]] of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The 't Hooft limit of $4-d$ ${\cal N} =4$ super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes are dual to various conformal field theories. This leads to a new proposal for a definition of [[0517 M-theory|M-theory]] which could be extended to include five non-compact dimensions.\] ## Refs - reviewed in [[1999#Aharony, Gubser, Maldacena, Ooguri, Oz]] - BI for non-Abelian theory -> [[1997#Tseytlin]] ## Low energy limit of open string perspective - $\alpha^\prime\rightarrow0$, $\kappa=g_S \alpha^{\prime2}\rightarrow0$ - $S=S_{\text {bulk }}+S_{\text {brane }}+S_{\text {int }}$ - interaction term (between brane modes and bulk modes) goes to zero - higher derivative terms in $S_\text{brane}$ goes to zero (so becomes SYM) - $S_\text{bulk}$ becomes a free supergravity theory - i.e. two theories decouple ## Low energy limit of SUGRA perspective - for infinite observer, two types of modes observed: long wavelength near infinity (do not feel the brane which has curvature length smaller than this wavelength) and near horizon modes of any energy (hard to climb up the potential; redshift makes any energy small at infinity) - two types decouple - long wavelength: free bulk supergravity in flat space - near-horizon: AdS${}_5\times S^5$ # Preskill ## Fault-tolerant quantum computation \[Links: [arXiv](https://arxiv.org/abs/quant-ph/9712048), [PDF](https://arxiv.org/pdf/quant-ph/9712048)\] \[Abstract: The discovery of [[0146 Quantum error correction|quantum error correction]] has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical operations. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. In principle, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per gate is less than a certain critical value, the accuracy threshold. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking topological Aharonov-Bohm interactions to process quantum information.\] # Strominger ## Black Hole Entropy from Near-Horizon Microstates \[Links: [arXiv](https://arxiv.org/abs/hep-th/9712251), [PDF](https://arxiv.org/pdf/hep-th/9712251.pdf)\] \[Abstract: Black holes whose near-horizon geometries are locally, but not necessarily globally, AdS$_3$ (three-dimensional anti-de Sitter space) are considered. Using the fact that quantum gravity on AdS$_3$ is a conformal field theory, we microscopically compute the [[0004 Black hole entropy|black hole entropy]] from the asymptotic growth of states. Precise numerical agreement with the Bekenstein-Hawking area formula for the entropy is found. The result pertains to any consistent quantum theory of gravity, and does not use string theory or supersymmetry.\] ## Refs - generalisation of the BH entropy calculation to 4D Kerr BH in [[2008#Guica, Hartman, Song, Strominger]] ## Summary - [[0086 Banados-Teitelboim-Zanelli black hole|BTZ entropy]] from [[0406 Cardy formula|Cardy formula]] # Tseytlin ## On non-abelian generalisation of Born-Infeld action in string theory \[Links: [arXiv](https://arxiv.org/abs/hep-th/9701125), [PDF](https://arxiv.org/pdf/hep-th/9701125.pdf)\] \[Abstract: We show that the part of the tree-level open string effective action for the non-abelian vector field which depends on the field strength but not on its covariant derivatives, is given by the symmetrised trace of the direct non-abelian generalisation of the Born-Infeld invariant. We discuss applications to D-brane dynamics.\] ## Summary - Born-Infeld action is the result of summing over all orders in the ==tree-level effective Lagrangian for open string theory== -> this paper does it for non-Abelian gauge groups ## Separation - $L_{e f f}=\operatorname{Tr}\left(a_{0} F^{2}+a_{1} F D^{2} F+a_{2} F^{4}+a_{3} F^{2} D^{2} F+\ldots\right)=L(F)+O(D F)$ - $L(F)$ is what we look for - treat all $[,]$ terms as $O(DF)$ terms - there is an ambiguity in the non-Abelian case in whether they belong to $L(F)$ or $O(DF)$ ## The result - Abelian (known before) - $L_{B I}=c_{0} \sqrt{\operatorname{det}\left(\delta_{m n}+T^{-1} F_{m n}\right)}, \quad T^{-1}=2 \pi \alpha^{\prime}$ - non-Abelian (this paper) - $L(F)=L_{N B I}=c_{0} \mathrm{STr} \sqrt{\operatorname{det}\left(\delta_{m n}+T^{-1} F_{m n}\right)}$