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Register a new userA General Prescription for Semi-Classical Holography
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We present a version of holographic correspondence where bulk solutions with sources localized on the holographic screen are the key objects of interest, and not bulk solutions defined by their boundary values on the screen. We can use this to calculate semi-classical holographic correlators in fairly general spacetimes, including flat space with timelike screens. We find that our approach reduces to the standard Dirichlet-like approach, when restricted to the boundary of AdS. But in more general settings, the analytic continuation of the Dirichlet Green function does not lead to a Feynman propagator in the bulk. Our prescription avoids this problem. Furthermore, in Lorentzian signature we find an additional homogeneous mode. This is a natural proxy for the AdS normalizable mode and allows us to do bulk reconstruction. We also find that the extrapolate and differential dictionaries match. Perturbatively adding bulk interactions to these discussions is straightforward. We conclude by elevating some of these ideas into a general philosophy about mechanics and field theory. We argue that localizing sources on suitable submanifolds can be an instructive alternative formalism to treating these submanifolds as boundaries.
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We present a general prescription for determining the global U(1) symmetries of six-dimensional superconformal field theories (6D SCFTs). We use the quiver-like gauge theory description of the tensor branch to identify candidate U(1) symmetries which can act on generalized matter. The condition that these candidate U(1)s are free of Adler-Bell-Jackiw (ABJ) anomalies provides bottom-up constraints for U(1)s. This agrees with the answer obtained from symmetry breaking patterns induced by Higgs branch flows. We provide numerous examples illustrating the details of this proposal. In the F-theory realization of these theories, some of these symmetries originate from deformations of non-abelian flavor symmetries localized on a component of the discriminant, while others come from an additional generator of the Mordell-Weil group. We also provide evidence that some of these global U(1)s do not arise from gauge symmetries, as would happen in taking a decoupling limit of a model coupled to six-dimensional supergravity.
A world-sheet sigma model approach is applied to string theories dual to four-dimensional gauge theories, and semi-classical soliton solutions representing highly excited string states are identified which correspond to gauge theory operators with relatively small anomalous dimensions. The simplest class of such states are strings on the leading Regge trajectory, with large spin in AdS_5. These correspond to operators with many covariant derivatives, whose anomalous dimension grows logarithmically with the space-time spin. In the gauge theory, the logarithmic scaling violations are similar to those found in perturbation theory. Other examples of highly excited string states are also considered.
Following earlier work, we view two dimensional non-linear sigma model with target space $cM$ as a single particle relativistic quantum mechanics in the corresponding free loop space $cLM$. In a natural semi-classical limit ($hbar=alpha to 0$) of this model the wavefunction localizes on the submanifold of vanishing loops which is isomorphic to $cM$. One would expect that the relevant semi-classical expansion should be related to the tubular expansion of the theory around the submanifold and an effective dynamics on the submanifold is obtainable using Born-Oppenheimer approximation. In this work we develop a framework to carry out such an analysis at the leading order in $alpha$-expansion. In particular, we show that the linearized tachyon effective equation is correctly reproduced up to divergent terms all proportional to the Ricci scalar of $cM$. The steps leading to this result are as follows: first we define a finite dimensional analogue of the loop space quantum mechanics (LSQM) where we discuss its tubular expansion and how that is related to a semi-classical expansion of the Hamiltonian. Then we study an explicit construction of the relevant tubular neighborhood in $cLM$ using exponential maps. Such a tubular geometry is obtained from a Riemannian structure on the tangent bundle of $cM$ which views the zero-section as a submanifold admitting a tubular neighborhood. Using this result and exploiting an analogy with the toy model we arrive at the final result for LSQM.
Drugs are frequently prescribed to patients with the aim of improving each patients medical state, but an unfortunate consequence of most prescription drugs is the occurrence of undesirable side effects. Side effects that occur in more than one in a thousand patients are likely to be signalled efficiently by current drug surveillance methods, however, these same methods may take decades before generating signals for rarer side effects, risking medical morbidity or mortality in patients prescribed the drug while the rare side effect is undiscovered. In this paper we propose a novel computational meta-analysis framework for signalling rare side effects that integrates existing methods, knowledge from the web, metric learning and semi-supervised clustering. The novel framework was able to signal many known rare and serious side effects for the selection of drugs investigated, such as tendon rupture when prescribed Ciprofloxacin or Levofloxacin, renal failure with Naproxen and depression associated with Rimonabant. Furthermore, for the majority of the drug investigated it generated signals for rare side effects at a more stringent signalling threshold than existing methods and shows the potential to become a fundamental part of post marketing surveillance to detect rare side effects.
Recently the bound on the Lyapunov exponent $lambda_L le 2pi T/ hbar$ in thermal quantum systems was conjectured by Maldacena, Shenker, and Stanford. If we naively apply this bound to a system with a fixed Lyapunov exponent $lambda_L$, it might predict the existence of the lower bound on temperature $T ge hbar lambda_L/ 2pi $. Particularly, it might mean that chaotic systems cannot be zero temperature quantum mechanically. Even classical dynamical systems, which are deterministic, might exhibit thermal behaviors once we turn on quantum corrections. We elaborate this possibility by investigating semi-classical particle motions near the hyperbolic fixed point and show that indeed quantum corrections may induce energy emission which obeys a Boltzmann distribution. We also argue that this emission is related to acoustic Hawking radiation in quantum fluid. Besides, we discuss when the bound is saturated and show that a particle motion in an inverse harmonic potential and $c=1$ matrix model may saturate the bound although they are integrable.
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