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132
Large N BPS states and emergent quantum gravity
, 2006
"... This paper provides a heuristic derivation of how classical gravitational physics in the AdS/CFT correspondence appears from the strong dynamics of the N = 4 SYM theory in a systematic way. We do this in a minisuperspace approximation by studying 1/8 BPS configurations. We can show that our descri ..."
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Cited by 97 (14 self)
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This paper provides a heuristic derivation of how classical gravitational physics in the AdS/CFT correspondence appears from the strong dynamics of the N = 4 SYM theory in a systematic way. We do this in a minisuperspace approximation by studying 1/8 BPS configurations. We can show that our description matches the semiclassical physics of 1/8 BPS states in supergravity. We also provide a heuristic description of how massive strings appear in the geometry, and how at strong ’t Hooft coupling they become local on the S 5 suggesting that they can be realized as a sigma model on a weakly curved background. We show that the dynamics of 1/8 BPS dynamics of N = 4 SYM on a round S 3 can be reduced to that of a matrix model for commuting matrices. Including measure factors, we show that this effective dynamics is related to bosons living on a six dimensional phase space with repulsive interactions. Because of these interactions, we can argue that on the ground state the bosons assemble themselves on a spherical shell in the shape of a round five sphere. This sphere will be identified with the S 5 in the AdS dual geometry. To do this, we first define a precise way to coarse grain the dynamics. We use half BPS configurations as a toy model for this coarse graining, and we can reproduce the droplet
Quantum search of spatial regions
 THEORY OF COMPUTING
, 2005
"... Can Grover’s algorithm speed up search of a physical region—for example a 2D grid of size √ n × √ n? The problem is that √ n time seems to be needed for each query, just to move amplitude across the grid. Here we show that this problem can be surmounted, refuting a claim to the contrary by Beniof ..."
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Cited by 84 (7 self)
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Can Grover’s algorithm speed up search of a physical region—for example a 2D grid of size √ n × √ n? The problem is that √ n time seems to be needed for each query, just to move amplitude across the grid. Here we show that this problem can be surmounted, refuting a claim to the contrary by Benioff. In particular, we show how to search a ddimensional hypercube in time O ( √ n) for d ≥ 3, or O ( √ nlog 5/2 n) for d = 2. More generally, we introduce a model of quantum query complexity on graphs, motivated by fundamental physical limits on information storage, particularly the holographic principle from black hole thermodynamics. Our results in this model include almosttight upper and lower bounds for many search tasks; a generalized algorithm that works for any graph with good expansion properties, not just hypercubes; and relationships among several notions of ‘locality’ for unitary matrices acting on graphs. As an application of our results, we give an O (√ n)qubit communication protocol for the disjointness problem, which improves an upper bound of Høyer and de Wolf and matches a lower bound of Razborov.
NPcomplete problems and physical reality
 ACM SIGACT News Complexity Theory Column, March. ECCC
, 2005
"... Can NPcomplete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantummechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Mal ..."
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Cited by 55 (6 self)
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Can NPcomplete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantummechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, MalamentHogarth spacetimes, quantum gravity, closed timelike curves, and “anthropic computing. ” The section on soap bubbles even includes some “experimental ” results. While I do not believe that any of the proposals will let us solve NPcomplete problems efficiently, I argue that by studying them, we can learn something not only about computation but also about physics. 1
Integrated information in discrete dynamical systems: motivation and theoretical framework
, 2008
"... This paper introduces a time and statedependent measure of integrated information, w, which captures the repertoire of causal states available to a system as a whole. Specifically, w quantifies how much information is generated (uncertainty is reduced) when a system enters a particular state throu ..."
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Cited by 41 (9 self)
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This paper introduces a time and statedependent measure of integrated information, w, which captures the repertoire of causal states available to a system as a whole. Specifically, w quantifies how much information is generated (uncertainty is reduced) when a system enters a particular state through causal interactions among its elements, above and beyond the information generated independently by its parts. Such mathematical characterization is motivated by the observation that integrated information captures two key phenomenological properties of consciousness: (i) there is a large repertoire of conscious experiences so that, when one particular experience occurs, it generates a large amount of information by ruling out all the others; and (ii) this information is integrated, in that each experience appears as a whole that cannot be decomposed into independent parts. This paper extends previous work on stationary systems and applies integrated information to discrete networks as a function of their dynamics and causal architecture. An analysis of basic examples indicates the following: (i) w varies depending on the state entered by a network, being higher if active and inactive elements are balanced and lower if the network is inactive or hyperactive. (ii) w varies for systems with identical or similar surface dynamics depending on the underlying causal architecture, being low for systems that merely copy or replay activity states. (iii) w varies as a function of network architecture. High w values can be obtained by architectures that conjoin functional specialization with functional integration. Strictly modular and homogeneous systems cannot generate high w
Rigorous steps towards holography in asymptotically flat spacetimes
 Rev. Math. Phys
"... Abstract. Scalar QFT on the boundary ℑ + at null infinity of a general asymptotically flat 4D spacetime is constructed using the algebraic approach based on Weyl algebra associated to a BMSinvariant symplectic form. The constructed theory turns out to be invariant under a suitable stronglycontinuous ..."
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Cited by 33 (16 self)
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Abstract. Scalar QFT on the boundary ℑ + at null infinity of a general asymptotically flat 4D spacetime is constructed using the algebraic approach based on Weyl algebra associated to a BMSinvariant symplectic form. The constructed theory turns out to be invariant under a suitable stronglycontinuous unitary representation of the BMS group with manifest meaning when the fields are interpreted as suitable extensions to ℑ + of massless minimally coupled fields propagating in the bulk. The group theoretical analysis of the found unitary BMS representation proves that such a field on ℑ + coincides with the natural wave function constructed out of the unitary BMS irreducible representation induced from the little group ∆, the semidirect product between SO(2) and the twodimensional translations group. This wave function is massless with respect to the notion of mass for BMS representation theory. The presented result proposes a natural criterion to solve the long standing problem of the topology of BMS group. Indeed the found natural correspondence of quantum field theories holds only if the BMS group is equipped with the nuclear topology rejecting instead the Hilbert one. Eventually some theorems towards a holographic description on ℑ + of QFT in the bulk are established at level of C ∗ algebras of fields for strongly asymptotically predictable spacetimes. It is proved that preservation of a certain symplectic form implies the existence of an injective ∗homomorphism from the Weyl algebra of fields of the bulk
The Unruh effect and its applications
, 2008
"... It has been 30 years since the discovery of the Unruh effect. It has played a crucial role in our understanding that the particle content of a field theory is observer dependent. This effect is important in its own right and as a way to understand the phenomenon of particle emission from black holes ..."
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Cited by 19 (0 self)
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It has been 30 years since the discovery of the Unruh effect. It has played a crucial role in our understanding that the particle content of a field theory is observer dependent. This effect is important in its own right and as a way to understand the phenomenon of particle emission from black holes and cosmological horizons. The Unruh effect is reviewed here with particular emphasis on its applications. A number of recent developments are also commented on and some controversies are discussed. Effort is also made to clarify what seem to be common misconceptions.
FRW solutions and holography from uplifted AdS/CFT, arXiv:1108.5732
, 2000
"... Starting from concrete AdS/CFT dual pairs, one can introduce ingredients which produce cosmological solutions, including metastable de Sitter and its decay to nonaccelerating FRW. We present simple FRW solutions sourced by magnetic flavor branes and analyze correlation functions and particle and bra ..."
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Cited by 18 (7 self)
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Starting from concrete AdS/CFT dual pairs, one can introduce ingredients which produce cosmological solutions, including metastable de Sitter and its decay to nonaccelerating FRW. We present simple FRW solutions sourced by magnetic flavor branes and analyze correlation functions and particle and brane dynamics. To obtain a holographic description, we exhibit a timedependent warped metric on the solution and interpret the resulting redshifted region as a Lorentzian low energy effective field theory in one fewer dimension. At finite times, this theory has a finite cutoff, a propagating lower dimensional graviton and a finite covariant entropy bound, but at late times the lower dimensional Planck mass and entropy go off to infinity in a way that is dominated by contributions from the low energy effective theory. This opens up the possibility of a precise dual at late times. We reproduce the timedependent growth of the number of degrees of freedom in the system via a count of available microscopic states in the corresponding magnetic brane construction. Work supported in part by US Department of Energy contract DEAC0276SF00515. Contents