# Balasubramanian, de Boer, Keski-Vakkuri, Ross ## SUSY conical defects: towards a string theoretic description of BH formation \[Links: [arXiv](https://arxiv.org/abs/hep-th/0011217), [PDF](https://arxiv.org/pdf/hep-th/0011217.pdf)\] \[Abstract: \] # Bekenstein ## On Page's examples challenging the entropy bound \[Links: [arXiv](https://arxiv.org/abs/gr-qc/0006003), [PDF](https://arxiv.org/pdf/gr-qc/0006003.pdf)\] \[Abstract: According to the [[0418 Bekenstein bound|entropy bound]], the entropy of a complete physical system can be universally bounded in terms of its circumscribing radius and total gravitating energy. Page's three recent candidates for counterexamples to the bound are here clarified and refuted by stressing that the energies of all essential parts of the system must be included in the energy the bound speaks about. Additionally, in response to an oft heard claim revived by Page, I give a short argument showing why the entropy bound is obeyed at low temperatures by a complete system. Finally, I remark that Page's renewed appeal to the venerable ''many species'' argument against the entropy bound seems to be inconsistent with quantum field theory.\] # Buric, Radovanovic ## Quantum corrections for (anti-)evaporating BH \[Links: [arXiv](https://arxiv.org/abs/hep-th/0007172), [PDF](https://arxiv.org/pdf/hep-th/0007172.pdf)\] \[Abstract: \] ## Refs - [[vapour_nonmin]] ## Summary - *calculates* backreaction of quantum matter analytically - *uses* two auxiliary fields to turn a non-local action to a local one - introduced earlier in [[BuricRadovanovicMikovic1998]][](https://arxiv.org/abs/gr-qc/9804083) ## Issues - did not deal with the anti-evaporation issue - should repeat this calculation by adding the correct terms that fixes it # Dijkgraaf, Maldacena, Moore, Verlinde ## A Black Hole Farey Tail \[Links: [arXiv](https://arxiv.org/abs/hep-th/0005003), [PDF](https://arxiv.org/pdf/hep-th/0005003.pdf)\] \[Abstract: We derive an exact expression for the Fourier coefficients of elliptic genera of Calabi-Yau manifolds. When applied to k-fold symmetric products of K3 surfaces the expression is well-suited to studying the AdS/CFT correspondence on AdS$_3 \times S^3$. The expression also elucidates an $\mathrm{SL}(2,Z)$ invariant phase diagram for the D1/D5 system involving deconfining transitions in the limit as $k$ goes to infinity.\] # Fateev, Zamolodchikov, Zamolodchikov ## Boundary Liouville Field Theory I. Boundary State and Boundary Two-point Function \[Links: [arXiv](https://arxiv.org/abs/hep-th/0001012), [PDF](https://arxiv.org/pdf/hep-th/0001012)\] \[Abstract: [[0562 Liouville theory|Liouville conformal field theory]] is considered with conformal boundary. There is a family of conformal boundary conditions parameterized by the boundary cosmological constant, so that observables depend on the dimensional ratios of boundary and bulk cosmological constants. The disk geometry is considered. We present an explicit expression for the expectation value of a bulk operator inside the disk and for the two-point function of boundary operators. We comment also on the properties of the degenrate boundary operators. Possible applications and further developments are discussed. In particular, we present exact expectation values of the boundary operators in the boundary sin-Gordon model.\] # Ford, Roman ## Classical scalar fields and the generalised second law \[Links: [arXiv](https://arxiv.org/abs/gr-qc/0009076), [PDF](https://arxiv.org/pdf/gr-qc/0009076.pdf)\] \[Abstract: \] ## Comments Wald formula still works with non-minimal fields for the Wald entropy; and here there is no anomaly term for this theory so the full entropy is just Wald entropy which satisfy a second law unsurprisingly. What is more interesting would be [[0338 Non-minimally coupled fields]] with an anomaly term, in which case one needs to find the correct [[0004 Black hole entropy|Gravitational entanglement entropy]] formula in a way similar to [[2015#Wall (Essay)]] and show that the [[0082 Generalised second law]] holds. This is shown already in [[2015#Wall (Essay)]] for non-minimally coupled scalars but for vector fields it is investigated in the project [[2ndlaw]]. ## Summary - [[0082 Generalised second law]] still holds for non-minimally coupled scalar field although they can provide lots of negative energy - two important effects that rescue GSL: - acausal behaviour of horizon - modification of the entropy formula ## Model - Lagrangian - $L=-\frac{1}{2}\left(g^{\mu \nu} \nabla_{\mu} \phi \nabla_{\nu} \phi+\xi R \phi^{2}+V(\phi)\right)$ - entropy - $S=\frac{A}{4}+4 \pi \int_{H} \frac{\partial \mathcal{L}}{\partial R} \sqrt{{ }_{2} g} d^{2} x$=\frac{A}{4}\left(1-8 \pi \xi\left\langle\phi^{2}\right\rangle\right)$ - $\left\langle\phi^{2}\right\rangle=\frac{1}{A} \int \phi^{2} \sqrt{{ }_{2} g} d^{2} x$ ## Technique - transformation from Jordan frame to Einstein frame <!-- ## Refs - recommended by #aronwall for [[2ndlaw]] ---> # Gao, Wald ## Theorems on gravitational time delay and related issues \[Links: [arXiv](https://arxiv.org/abs/gr-qc/0007021), [PDF](https://arxiv.org/pdf/gr-qc/0007021.pdf)\] \[Abstract: \] ## Refs - [[0477 Gao-Wald theorem]] - [[0091 Boundary causality]] # Gottesman, Kitaev, Preskill ## Encoding a qubit in an oscillator \[Links: [arXiv](https://arxiv.org/abs/quant-ph/0008040), [PDF](https://arxiv.org/pdf/quant-ph/0008040.pdf)\] \[Abstract: [[0146 Quantum error correction|Quantum error-correcting codes]] are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables $q$ and $p$. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a $d$-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.\] # Krasnov ## Holography and Riemann Surfaces \[Links: [arXiv](https://arxiv.org/abs/hep-th/0005106), [PDF](https://arxiv.org/pdf/hep-th/0005106)\] \[Abstract: We study holography for asymptotically AdS spaces with an arbitrary genus compact Riemann surface as the conformal boundary. Such spaces can be constructed from the Euclidean AdS$_3$ by discrete identifications; the discrete groups one uses are the so-called classical Schottky groups. As we show, the spaces so constructed have an appealing interpretation of ''analytic continuations'' of the known Lorentzian signature black hole solutions; it is one of the motivations for our generalization of the holography to this case. We use the semi-classical approximation to the gravity path integral, and calculate the gravitational action for each space, which is given by the (appropriately regularized) volume of the space. As we show, the [[0209 Holographic renormalisation|regularized]] volume reproduces exactly the action of [[0562 Liouville theory|Liouville theory]], as defined on arbitrary Riemann surfaces by Takhtajan and Zograf. Using the results as to the properties of this action, we discuss thermodynamics of the spaces and analyze the boundary CFT partition function. Some aspects of our construction, such as the thermodynamical interpretation of the Teichmuller (Schottky) spaces, may be of interest for mathematicians working on Teichmuller theory.\] # Lazaroiu ## On the structure of open-closed topological field theory in two dimensions \[Links: [arXiv](https://arxiv.org/abs/hep-th/0010269), [PDF](https://arxiv.org/pdf/hep-th/0010269)\] \[Abstract: I discuss the general formalism of two-dimensional topological field theories defined on [[0625 Open-closed TQFT|open-closed]] oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for the identification of the algebraic structure governing such systems. I give a careful treatment of bulk-boundary and boundary-bulk correspondences, which are responsible for the relation between the closed and open sectors. The fact that these correspondences need not be injective nor surjective has interesting implications for the problem of classifying 'boundary conditions'. In particular, I give a clear geometric derivation of the (topological) boundary state formalism and point out some of its limitations. Finally, I formulate the problem of classifying (on-shell) boundary extensions of a given closed topological field theory in purely algebraic terms and discuss their reducibility.\] # Louko, Marolf, Ross ## On geodesic propagators and black hole holography \[Links: [arXiv](https://arxiv.org/abs/hep-th/0002111), [PDF](https://arxiv.org/pdf/hep-th/0002111.pdf)\] \[Abstract: \] ## Refs - earlier work on detecting particles in the bulk [[1999#Balasubramanian, Ross]] ## Summary - study [[0103 Two-point functions|propagator]] for BTZ and single exterior black hole - issues of causality, horizons, the products of operators on the boundary - in particular, stationary phase approximation in [[1999#Balasubramanian, Ross]] is wrong, but it is fine if we work in some nice analytic spacetimes ## Basics - scale-radius duality - a consequence of isometry in AdS - not true in general - non-local information - some solutions have the same asymptotic behaviour - can distinguish by non-local operator expectations values in CFT - examples - 2-pt functions - Wilson loops ## Causality issues - propagator should not know about the interior - resolution: stationary phase approximation fails - however, it may be possible to choose a state of states such that the 2-pt function does reproduce features behind the horizon - such states would involve a mixture of both initial and final conditions! ## Propagator - $\left\langle\phi(x) \phi(x^{\prime})\right\rangle_{\mathrm{FPI}}=\int d \mathcal{P} e^{i \Delta L(\mathcal{P})}$ - convention: real length for timelike paths, and imaginary for spacelike - problem: what is the state of the linearised field in the bulk # Maldacena, Ooguri ## Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum \[Links: [arXiv](https://arxiv.org/abs/hep-th/0001053), [PDF](https://arxiv.org/pdf/hep-th/0001053.pdf)\] \[Abstract: \] ## Refs - [[0344 Tensionless string]] ## Spectral flow - takes some representation to some other representation # Moore (Talk) ## Some Comments on Branes, G-flux, and K-theory \[Links: [arXiv](https://arxiv.org/abs/hep-th/0012007), [PDF](https://arxiv.org/pdf/hep-th/0012007)\] \[Abstract: This is a summary of a talk at Strings2000 explaining three ways in which string theory and M-theory are related to the mathematics of K-theory.\] # Ponsot, Teschner ## Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of $U_q(sl(2,R))$ \[Links: [arXiv](https://arxiv.org/abs/math/0007097), [PDF](https://arxiv.org/pdf/math/0007097.pdf)\] \[Abstract: The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of $U_q(sl(2,R)$. It is described by an explicit integral transformation involving a distributional kernel that can be seen as an analogue of the Clebsch-Gordan coefficients. Moreover, we also study the relation between two canonical decompositions of triple tensor products into irreducibles. It can be represented by an integral transformation with a kernel that generalizes the Racah-Wigner coefficients. This kernel is explicitly calculated.\] # Scharlemann ## Heegaard splittings of compact 3-manifolds \[Links: [arXiv](https://arxiv.org/abs/math/0007144), [PDF](https://arxiv.org/pdf/math/0007144.pdf)\] \[Abstract: An expository survey article on Heegaard splittings.\] # Teschner ## Remarks on Liouville theory with boundary \[Links: [arXiv](https://arxiv.org/abs/hep-th/0009138), [PDF](https://arxiv.org/pdf/hep-th/0009138)\] \[Abstract: The bootstrap for [[0562 Liouville theory|Liouville theory]] with conformally invariant boundary conditions will be discussed. After reviewing some results on one- and boundary two-point functions we discuss some analogue of the Cardy condition linking these data. This allows to determine the spectrum of the theory on the strip, and illustrates in what respects the bootstrap for noncompact conformal field theories with boundary is richer than in RCFT. We briefly indicate some connections with $U_q(sl(2,R))$ that should help completing the bootstrap.\] # van den Brink ## Analytic treatment of black-hole gravitational waves at the algebraically special frequency \[Links: [arXiv](https://arxiv.org/abs/gr-qc/0001032), [PDF](https://arxiv.org/pdf/gr-qc/0001032.pdf)\] \[Abstract: We study the Regge-Wheeler and Zerilli equations (RWE and ZE) at the 'algebraically special frequency' $\Omega$, where these equations admit an exact solution (elaborated here), generating the SUSY relationship between them. The physical significance of the SUSY generator and of the solutions at $\Omega$ in general is elucidated as follows. The RWE has no (quasinormal or total-transmission) modes at all; however, $\Omega$ is nonetheless 'special' in that (a) for the outgoing wave into the horizon one has a 'miraculous' cancellation of a divergence expected due to the exponential potential tail, and (b) the branch-cut discontinuity at $\omega=\Omega$ vanishes in the outgoing wave to infinity. Moreover, (a) and (b) are related. For the ZE, its only mode is the-inverse-SUSY generator, which is at the same time a quasinormal mode *and* a total-transmission mode propagating to infinity. The subtlety of these findings (of general relevance for future study of the equations on or near the negative imaginary $\omega$-axis) may help explain why the situation has sometimes been controversial. For finite black-hole rotation, the algebraically special modes are shown to be totally transmitting, and the implied singular nature of the Schwarzschild limit is clarified. The analysis draws on a recent detailed investigation of SUSY in open systems [[math-ph/9909030](https://arxiv.org/abs/math-ph/9909030)].\] # Visser, Bassett, Liberati ## Superluminal censorship \[Links: [arXiv](https://arxiv.org/abs/gr-qc/9810026), [PDF](https://arxiv.org/pdf/gr-qc/9810026.pdf)\] \[Abstract: We argue that ''effective'' superluminal travel, potentially caused by the tipping over of light cones in Einstein gravity, is always associated with violations of the [[0480 Null energy condition|null energy condition]] (NEC). This is most easily seen by working perturbatively around Minkowski spacetime, where we use linearized Einstein gravity to show that the NEC forces the light cones to contract (narrow). Given the NEC, the Shapiro time delay in any weak gravitational field is always a delay relative to the Minkowski background, and never an advance. Furthermore, any object travelling within the lightcones of the weak gravitational field is similarly delayed with respect to the minimum traversal time possible in the background Minkowski geometry.\]